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1. A complete classification of the expressiveness of interval logics of Allen’s relations Aceto, Lucaet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt1277",{id:"formSmash:items:resultList:0:j_idt1277",widgetVar:"widget_formSmash_items_resultList_0_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Della Monica, DarioGoranko, ValentinStockholms universitet, Humanistiska fakulteten, Filosofiska institutionen. University of Johannesburg, South Africa.Ingólfsdóttir, AnnaMontanari, AngeloSciavicco, GuidoPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A complete classification of the expressiveness of interval logics of Allen’s relations: the general and the dense cases2016Inngår i: Acta Informatica, ISSN 0001-5903, E-ISSN 1432-0525, Vol. 53, nr 3, s. 207-246Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:0:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_0_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Interval temporal logics take time intervals, instead of time points, as their primitive temporal entities. One of the most studied interval temporal logics is Halpern and Shoham’s modal logic of time intervals HS, which associates a modal operator with each binary relation between intervals over a linear order (the so-called Allen’s interval relations). In this paper, we compare and classify the expressiveness of all fragments of HS on the class of all linear orders and on the subclass of all dense linear orders. For each of these classes, we identify a complete set of definabilities between HS modalities, valid in that class, thus obtaining a complete classification of the family of all 4096 fragments of HS with respect to their expressiveness. We show that on the class of all linear orders there are exactly 1347 expressively different fragments of HS, while on the class of dense linear orders there are exactly 966 such expressively different fragments.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 2. Displayed Categories Ahrens, Benediktet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1277",{id:"formSmash:items:resultList:1:j_idt1277",widgetVar:"widget_formSmash_items_resultList_1_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lumsdaine, Peter LefanuStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Displayed Categories2019Inngår i: Logical Methods in Computer Science, ISSN 1860-5974, E-ISSN 1860-5974, Vol. 15, nr 1, artikkel-id 20Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:1:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_1_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We introduce and develop the notion of displayed categories. A displayed category over a category C is equivalent to 'a category D and functor F : D -> C', but instead of having a single collection of 'objects of D' with a map to the objects of C, the objects are given as a family indexed by objects of C, and similarly for the morphisms. This encapsulates a common way of building categories in practice, by starting with an existing category and adding extra data/properties to the objects and morphisms. The interest of this seemingly trivial reformulation is that various properties of functors are more naturally defined as properties of the corresponding displayed categories. Grothendieck fibrations, for example, when defined as certain functors, use equality on objects in their definition. When defined instead as certain displayed categories, no reference to equality on objects is required. Moreover, almost all examples of fibrations in nature are, in fact, categories whose standard construction can be seen as going via displayed categories. We therefore propose displayed categories as a basis for the development of fibrations in the type-theoretic setting, and similarly for various other notions whose classical definitions involve equality on objects. Besides giving a conceptual clarification of such issues, displayed categories also provide a powerful tool in computer formalisation, unifying and abstracting common constructions and proof techniques of category theory, and enabling modular reasoning about categories of multi-component structures. As such, most of the material of this article has been formalised in Coq over the UniMath library, with the aim of providing a practical library for use in further developments.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 3. Contributions to certain problems in algebraic topology Alonso, Juan M. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt1274",{id:"formSmash:items:resultList:2:j_idt1274",widgetVar:"widget_formSmash_items_resultList_2_j_idt1274",onLabel:"Alonso, Juan M. ",offLabel:"Alonso, Juan M. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Contributions to certain problems in algebraic topology1984Doktoravhandling, med artikler (Annet vitenskapelig)4. Homotopy limits in type theory Avigad, Jeremy PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1274",{id:"formSmash:items:resultList:3:j_idt1274",widgetVar:"widget_formSmash_items_resultList_3_j_idt1274",onLabel:"Avigad, Jeremy ",offLabel:"Avigad, Jeremy ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1277",{id:"formSmash:items:resultList:3:j_idt1277",widgetVar:"widget_formSmash_items_resultList_3_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Philosophy and Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania, U.S.A..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kapulkin, KrzysztofDepartment of Mathematics, University of Pittsburgh, Pennsylvania, U.S.A..Lumsdaine, Peter LeFanuInstitute for Advanced Study, Princeton, New Jersey, U.S.A..PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homotopy limits in type theory2015Inngår i: Mathematical Structures in Computer Science, ISSN 0960-1295, E-ISSN 1469-8072, Vol. 25, nr 5, s. 1040-1070Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:3:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_3_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Working in homotopy type theory, we provide a systematic study of homotopy limits of diagrams over graphs, formalized in the Coq proof assistant. We discuss some of the challenges posed by this approach to formalizing homotopy-theoretic material. We also compare our constructions with the more classical approach to homotopy limits via fibration categories.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:3:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 5. A cubical model of homotopy type theory Awodey, Steve PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt1274",{id:"formSmash:items:resultList:4:j_idt1274",widgetVar:"widget_formSmash_items_resultList_4_j_idt1274",onLabel:"Awodey, Steve ",offLabel:"Awodey, Steve ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Carnegie Mellon University, USA.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A cubical model of homotopy type theory2016Rapport (Annet vitenskapelig)Fulltekst (pdf)Awodey-Stockholm-Lectures-2016$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_4_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:4:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_4_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:4:j_idt1537:0:fullText"});}); 6. On a class of power ideals Backelin, Jörgen PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1274",{id:"formSmash:items:resultList:5:j_idt1274",widgetVar:"widget_formSmash_items_resultList_5_j_idt1274",onLabel:"Backelin, Jörgen ",offLabel:"Backelin, Jörgen ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1277",{id:"formSmash:items:resultList:5:j_idt1277",widgetVar:"widget_formSmash_items_resultList_5_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Oneto, AlessandroStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On a class of power ideals2015Inngår i: Journal of Pure and Applied Algebra, ISSN 0022-4049, E-ISSN 1873-1376, Vol. 219, nr 8, s. 3158-3180Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:5:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_5_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper we study the class of power ideals generated by the k(n) forms (x(0) + xi(g1) x(1) + ... + xi(gn) x(n))((k-1)d) where xi is a fixed primitive kth-root of unity and 0 <= g(j) <= k - 1 for all j. For k = 2, by using a Z(k)(n+1)-grading on C[x(0),..., x(n)], we compute the Hilbert series of the associated quotient rings via a simple numerical algorithm. We also conjecture the extension for k > 2. Via Macaulay duality, those power ideals are related to schemes of fat points with support on the k(n) points [1 : xi(g1) : ... : xi(gn)] in P-n. We compute Hilbert series, Betti numbers and Grobner basis for these 0-dimensional schemes. This explicitly determines the Hilbert series of the power ideal for all k: that this agrees with our conjecture for k > 2 is supported by several computer experiments.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_5_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:5:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_5_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:5:j_idt1537:0:fullText"});}); 7. Configuration spaces, props and wheel-free deformation quantization Backman, Theo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt1274",{id:"formSmash:items:resultList:6:j_idt1274",widgetVar:"widget_formSmash_items_resultList_6_j_idt1274",onLabel:"Backman, Theo ",offLabel:"Backman, Theo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Configuration spaces, props and wheel-free deformation quantization2016Doktoravhandling, monografi (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:6:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_6_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The main theme of this thesis is higher algebraic structures that come from operads and props.

The first chapter is an introduction to the mathematical framework needed for the content of this thesis. The chapter does not contain any new results.

The second chapter is concerned with the construction of a configuration space model for a particular 2-colored differential graded operad encoding the structure of two

*A*algebras with two_{∞}*A*morphisms and a homotopy between the morphisms. The cohomology of this operad is shown to be the well-known 2-colored operad encoding the structure of two associative algebras and of an associative algebra morphism between them._{∞}The third chapter is concerned with deformation quantization of (potentially) infinite dimensional (quasi-)Poisson manifolds. Our proof employs a variation on the

*transcendental*methods pioneered by M. Kontsevich for the finite dimensional case. The first proof of the infinite dimensional case is due to B. Shoikhet. A key feature of the first proof is the construction of a universal*L*structure on formal polyvector fields. Our contribution is a simplification of B. Shoikhet proof by considering a more natural configuration space and a simpler choice of_{∞}*propagator*. The result is also put into a natural context of the dg Lie algebras coming from graph complexes; the*L*structure is proved to come from a Maurer-Cartan element in the_{∞}*oriented graph complex*.The fourth chapter also deals with deformation quantization of (quasi-)Poisson structures in the infinite dimensional setting. Unlike the previous chapter, the methods used here are purely algebraic. Our main theorem is the possibility to deformation quantize quasi-Poisson structures by only using perturbative methods; in contrast to the transcendental methods employed in the previous chapter. We give two proofs of the theorem via the theory of dg operads, dg properads and dg props. We show that there is a dg prop morphism from a prop governing star-products to a dg prop(erad) governing (quasi-)Poisson structures. This morphism gives a theorem about the existence of a deformation quantization of (quasi-)Poisson structure. The proof proceeds by giving an explicit deformation quantization of

*s**uper-involutive Lie bialgebras*and then lifting that to the dg properad governing quasi-Poisson structures. The prop governing star-products was first considered by S.A. Merkulov, but the properad governing quasi-Poisson structures is a new construction.The second proof of the theorem employs the Merkulov-Willwacher polydifferential functor to transfer the problem of finding a morphism of dg props to that of finding a morphism of dg operads.We construct an extension of the well known operad of

*A*algebras such that the representations of it in_{∞}*V*are equivalent to an*A*structure on_{∞}*V*[[*ħ*]]. This new operad is also a minimal model of an operad that can be seen as the extension of the operad of associative algebras by a unary operation. We give an explicit map of operads from the extended associative operad to the operad we get when applying the Merkulov-Willwacher polydifferential functor to the properad of super-involutive Lie bialgebras. Lifting this map so as to go between their respective models gives a new proof of the main theorem.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:6:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_6_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:6:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_6_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:6:j_idt1537:0:fullText"});}); Download (jpg)Omslagsframsida$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_6_j_idt1541_0_j_idt1544",{id:"formSmash:items:resultList:6:j_idt1541:0:j_idt1544",widgetVar:"widget_formSmash_items_resultList_6_j_idt1541_0_j_idt1544",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:6:j_idt1541:0:otherAttachment"});}); 8. Connectivity through bounds for the Castelnuovo–Mumford regularity Balletti, Gabriele PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt1274",{id:"formSmash:items:resultList:7:j_idt1274",widgetVar:"widget_formSmash_items_resultList_7_j_idt1274",onLabel:"Balletti, Gabriele ",offLabel:"Balletti, Gabriele ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Connectivity through bounds for the Castelnuovo–Mumford regularity2017Inngår i: Journal of combinatorial theory. Series A (Print), ISSN 0097-3165, E-ISSN 1096-0899, Vol. 147, s. 46-54Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:7:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_7_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this note we generalize and unify two results on connectivity of graphs: one by Balinsky and Barnette, one by Athanasiadis. This is done through a simple proof using commutative algebra tools. In particular we use bounds for the Castelnuovo-Mumford regularity of their Stanley-Reisner rings. As a result, if Delta is a simplicial d-pseudomanifold and s is the largest integer such that A has a missing face of size s, then the 1-skeleton of Delta is inverted right perpendicular(s)/((s+1)d)inverted left perpendicular-connected. We also show that this value is tight.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_7_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:7:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_7_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:7:j_idt1537:0:fullText"});}); 9. The HoTT Library Bauer, Andrejet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt1277",{id:"formSmash:items:resultList:8:j_idt1277",widgetVar:"widget_formSmash_items_resultList_8_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Gross, JasonLeFanu Lumsdaine, PeterStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.Shulman, MichaelSozeau, MatthieuSpitters, BasPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The HoTT Library: A formalization of homotopy type theory in Coq2017Inngår i: Proceedings of the 6th ACM SIGPLAN Conference on Certified Programs and Proofs / [ed] Yves Bertot, Viktor Vafeiadis, New York, NY, USA: Association for Computing Machinery (ACM), 2017, s. 164-172Konferansepaper (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:8:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_8_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We report on the development of the HoTT library, a formalization of homotopy type theory in the Coq proof assistant. It formalizes most of basic homotopy type theory, including univalence, higher inductive types, and significant amounts of synthetic homotopy theory, as well as category theory and modalities. The library has been used as a basis for several independent developments. We discuss the decisions that led to the design of the library, and we comment on the interaction of homotopy type theory with recently introduced features of Coq, such as universe polymorphism and private inductive types.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Homological perturbation theory for algebras over operads Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt1274",{id:"formSmash:items:resultList:9:j_idt1274",widgetVar:"widget_formSmash_items_resultList_9_j_idt1274",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homological perturbation theory for algebras over operads2014Inngår i: Algebraic and Geometric Topology, ISSN 1472-2747, E-ISSN 1472-2739, Vol. 14, nr 5, s. 2511-2548Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:9:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_9_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We extend homological perturbation theory to encompass algebraic structures governed by operads and cooperads. The main difficulty is to find a suitable notion of algebra homotopy that generalizes to algebras over operads O . To solve this problem, we introduce thick maps of O –algebras and special thick maps that we call pseudo-derivations that serve as appropriate generalizations of algebra homotopies for the purposes of homological perturbation theory.

As an application, we derive explicit formulas for transferring Ω(C) –algebra structures along contractions, where C is any connected cooperad in chain complexes. This specializes to transfer formulas for O ∞ –algebras for any Koszul operad O , in particular for A ∞ –, C ∞ –, L ∞ – and G ∞ –algebras. A key feature is that our formulas are expressed in terms of the compact description of Ω(C) –algebras as coderivation differentials on cofree C –coalgebras. Moreover, we get formulas not only for the transferred structure and a structure on the inclusion, but also for structures on the projection and the homotopy

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Koszul A<sub>∞</sub>-algebras and free loop space homology Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt1274",{id:"formSmash:items:resultList:10:j_idt1274",widgetVar:"widget_formSmash_items_resultList_10_j_idt1274",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt1277",{id:"formSmash:items:resultList:10:j_idt1277",widgetVar:"widget_formSmash_items_resultList_10_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Börjeson, KajStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Koszul A_{∞}-algebras and free loop space homologyManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:10:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_10_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We introduce a notion of Koszul A

_{∞}-algebra that generalizes Priddy’s notion of a Koszul algebra and we use it to construct small A_{∞}- algebra models for Hochschild cochains. As an application, this yields new techniques for computing free loop space homology algebras of manifolds that are either formal or coformal (over a field or over the integers). We illustrate these techniques in two examples.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 12. Homotopic Hopf-Galois extensions revisited Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1274",{id:"formSmash:items:resultList:11:j_idt1274",widgetVar:"widget_formSmash_items_resultList_11_j_idt1274",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1277",{id:"formSmash:items:resultList:11:j_idt1277",widgetVar:"widget_formSmash_items_resultList_11_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hess, KathrynPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homotopic Hopf-Galois extensions revisitedManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:11:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_11_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this article we revisit the theory of homotopic Hopf-Galois extensions introduced in arXiv:0902.3393v2 [math.AT], in light of the homotopical Morita theory of comodules established in arXiv:1411.6517 [math.AT]. We generalize the theory to a relative framework, which we believe is new even in the classical context and which is essential for treating the Hopf-Galois correspondence in forthcoming work of the second author and Karpova. We study in detail homotopic Hopf-Galois extensions of differential graded algebras over a commutative ring, for which we establish a descent-type characterization analogous to the one Rognes provided in the context of ring spectra. An interesting feature in the differential graded setting is the close relationship between homotopic Hopf-Galois theory and Koszul duality theory. We show that nice enough principal fibrations of simplicial sets give rise to homotopic Hopf-Galois extensions in the differential graded setting, for which this Koszul duality has a familiar form.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 13. Homotopical Morita theory for corings Berglund, Alexander PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt1274",{id:"formSmash:items:resultList:12:j_idt1274",widgetVar:"widget_formSmash_items_resultList_12_j_idt1274",onLabel:"Berglund, Alexander ",offLabel:"Berglund, Alexander ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt1277",{id:"formSmash:items:resultList:12:j_idt1277",widgetVar:"widget_formSmash_items_resultList_12_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hess, KathrynPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homotopical Morita theory for coringsManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:12:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_12_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A coring (A,C) consists of an algebra A and a coalgebra C in the monoidal category of A-bimodules. Corings and their comodules arise naturally in the study of Hopf-Galois extensions and descent theory, as well as in the study of Hopf algebroids. In this paper, we address the question of when two corings in a symmetric monoidal model category V are homotopically Morita equivalent, i.e., when their respective categories of comodules are Quillen equivalent. The category of comodules over the trivial coring (A,A) is isomorphic to the category of A-modules, so the question above englobes that of when two algebras are homotopically Morita equivalent. We discuss this special case in the first part of the paper, extending previously known results. To approach the general question, we introduce the notion of a 'braided bimodule' and show that adjunctions between A-Mod and B-Mod that lift to adjunctions between (A,C)-Comod and (B,D)-Comod correspond precisely to braided bimodules between (A,C) and (B,D). We then give criteria, in terms of homotopic descent, for when a braided bimodule induces a Quillen equivalence. In particular, we obtain criteria for when a morphism of corings induces a Quillen equivalence, providing a homotopic generalization of results by Hovey and Strickland on Morita equivalences of Hopf algebroids. To illustrate the general theory, we examine homotopical Morita theory for corings in the category of chain complexes over a commutative ring.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:12:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 14. Cohomology of the moduli space of curves of genus three with level two structure Bergvall, Olof PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt1274",{id:"formSmash:items:resultList:13:j_idt1274",widgetVar:"widget_formSmash_items_resultList_13_j_idt1274",onLabel:"Bergvall, Olof ",offLabel:"Bergvall, Olof ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Cohomology of the moduli space of curves of genus three with level two structure2014Licentiatavhandling, monografi (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:13:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_13_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this thesis we investigate the moduli space M

_{3}[2] of curves of genus 3 equipped with a symplectic level 2 structure. In particular, we are interested in the cohomology of this space. We obtain cohomological information by decomposing M_{3}[2] into a disjoint union of two natural subspaces, Q[2] and H_{3}[2], and then making S_{7}- resp. S_{8}-equivariantpoint counts of each of these spaces separately.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:13:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_13_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:13:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_13_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:13:j_idt1537:0:fullText"});}); 15. Parametricity, automorphisms of the universe, and excluded middle Booij, Auke PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt1274",{id:"formSmash:items:resultList:14:j_idt1274",widgetVar:"widget_formSmash_items_resultList_14_j_idt1274",onLabel:"Booij, Auke ",offLabel:"Booij, Auke ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt1277",{id:"formSmash:items:resultList:14:j_idt1277",widgetVar:"widget_formSmash_items_resultList_14_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Birmingham.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Escardó, MartínUniversity of Birmingham.Lumsdaine, Peter LeFanuStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.Shulman, MichaelUniversity of San Diego.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Parametricity, automorphisms of the universe, and excluded middleManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:14:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_14_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); It is known that one can construct non-parametric functions by assuming classical axioms. Our work is a converse to that: we prove classical axioms in dependent type theory assuming specific instances of non-parametricity. We also address the interaction between classical axioms and the existence of automorphisms of a type universe. We work over intensional Martin-Löf dependent type theory, and in some results assume further principles including function extensionality, propositional extensionality, propositional truncation, and the univalence axiom.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 16. A Natural Interpretation of Classical Proofs Brage, Jens PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt1274",{id:"formSmash:items:resultList:15:j_idt1274",widgetVar:"widget_formSmash_items_resultList_15_j_idt1274",onLabel:"Brage, Jens ",offLabel:"Brage, Jens ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Natural Interpretation of Classical Proofs2006Doktoravhandling, monografi (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:15:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_15_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.

We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. This representation brings LK to a manageable form that allows us to split the succedent rules into parts. In this way, every succedent rule gives rise to a natural deduction style introduction rule. These introduction rules, taken together with the antecedent rules adapted to natural deduction, yield a natural deduction calculus whose subsequent interpretation in constructive type theory gives meaning to classical logic.

The Gentzen-Prawitz inversion principle holds for the introduction and elimination rules of the natural deduction calculus and allows for a corresponding notion of convertibility. We take the introduction rules to determine the meanings of the logical constants of classical logic and use the induced type-theoretic elimination rules to interpret the elimination rules of the natural deduction calculus. This produces an interpretation injective with respect to convertibility, contrary to an analogous translation into intuitionistic predicate logic.

From the interpretation in constructive type theory and the interpretation of cut by explicit substitution, we derive a full precision contraction relation for a natural deduction version of LK. We use a term notation to formalize the contraction relation and the corresponding cut-elimination procedure.

The interpretation can be read as a Brouwer-Heyting-Kolmogorov (BHK) semantics that justifies classical logic. The BHK semantics utilizes a notion of classical proof and a corresponding notion of classical truth akin to Kolmogorov's notion of pseudotruth. We also consider a second BHK semantics, more closely connected with Kolmogorov's double-negation translation.

The first interpretation reinterprets the consequence relation while keeping the constructive interpretation of truth, whereas the second interpretation reinterprets the notion of truth while keeping the constructive interpretation of the consequence relation. The first and second interpretations act on derivations in much the same way as Plotkin's call-by-value and call-by-name continuation-passing-style translations, respectively.

We conclude that classical logic can be given a constructive semantics by laying down introduction rules for the classical logical constants. This semantics constitutes a proof interpretation of classical logic.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:15:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_15_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:15:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_15_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:15:j_idt1537:0:fullText"});}); 17. Logics for reasoning about strategic abilities in multi-player games Bulling, Nilset al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt1277",{id:"formSmash:items:resultList:16:j_idt1277",widgetVar:"widget_formSmash_items_resultList_16_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Goranko, ValentinStockholms universitet, Humanistiska fakulteten, Filosofiska institutionen.Jamroga, WojciechPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Logics for reasoning about strategic abilities in multi-player games2015Inngår i: Models of strategic reasoning: logics, games and communities / [ed] Johan van Benthem, Sujata Ghosh, Rineke Verbrugge, Berlin: Springer, 2015, s. 93-136Kapittel i bok, del av antologi (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:16:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_16_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We introduce and discuss basic concepts, ideas, and logical formalisms used for reasoning about strategic abilities in multi-player games. In particular, we present concurrent game models and the alternating time temporal logic ATL∗ and its fragment ATL. We discuss variations of the language and semantics of ATL∗ that take into account the limitations and complications arising from incomplete information, perfect or imperfect memory of players, reasoning within dynamically changing strategy contexts, or using stronger, constructive concepts of strategy. Finally, we briefly summarize some technical results regarding decision problems for some variants of ATL.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:16:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 18. A Algebras Derived from Associative Algebras with a Non-Derivation Differential Börjeson, Kaj PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt1274",{id:"formSmash:items:resultList:17:j_idt1274",widgetVar:"widget_formSmash_items_resultList_17_j_idt1274",onLabel:"Börjeson, Kaj ",offLabel:"Börjeson, Kaj ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Algebras Derived from Associative Algebras with a Non-Derivation Differential2015Inngår i: Journal of Generalized Lie Theory and Applications, ISSN 1736-5279, E-ISSN 1736-4337, Vol. 9, nr 1, artikkel-id 214Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:17:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_17_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Given an associative graded algebra equipped with a degree +1 differential delta we define an A

_{∞}-structure that measures the failure of delta to be a derivation. This can be seen as a non-commutative analog of generalized BV-algebras. In that spirit we introduce a notion of associative order for the operator delta and prove that it satisfies properties similar to the commutative case. In particular when it has associative order 2 the new product is a strictly associative product of degree +1 and there is compatibility between the products, similar to ordinary BV-algebras. We consider several examples of structures obtained in this way. In particular we obtain an A_{∞}-structure on the bar complex of an A_{∞}-algebra that is strictly associative if the original algebra is strictly associative. We also introduce strictly associative degree +1 products for any degree +1 action on a graded algebra. Moreover, an A∞-structure is constructed on the Hochschild cocomplex of an associative algebra with a non-degenerate inner product by using Connes’ B-operator.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:17:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 19. Free loop spaces, Koszul duality and A-infinity algebras Börjeson, Kaj PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt1274",{id:"formSmash:items:resultList:18:j_idt1274",widgetVar:"widget_formSmash_items_resultList_18_j_idt1274",onLabel:"Börjeson, Kaj ",offLabel:"Börjeson, Kaj ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Free loop spaces, Koszul duality and A-infinity algebras2017Doktoravhandling, med artikler (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:18:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_18_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This thesis consists of four papers on the topics of free loop spaces, Koszul duality and A

_{∞}-algebras.In Paper I we consider a definition of differential operators for noncommutative algebras. This definition is inspired by the connections between differential operators of commutative algebras, L

_{∞}-algebras and BV-algebras. We show that the definition is reasonable by establishing results that are analoguous to results in the commutative case. As a by-product of this definition we also obtain definitions for noncommutative versions of Gerstenhaber and BV-algebras.In Paper II we calculate the free loop space homology of (n-1)-connected manifolds of dimension of at least 3n-2. The Chas-Sullivan loop product and the loop bracket are calculated. Over a field of characteristic zero the BV-operator is determined as well. Explicit expressions for the Betti numbers are also established, showing that they grow exponentially.

In Paper III we restrict our coefficients to a field of characteristic 2. We study the Dyer-Lashof operations that exist on free loop space homology in this case. Explicit calculations are carried out for manifolds that are connected sums of products of spheres.

In Paper IV we extend the Koszul duality methods used in Paper II by incorporating A

_{∞}-algebras and A_{∞}-coalgebras. This extension of Koszul duality enables us to compute free loop space homology of manifolds that are not necessarily formal and coformal. As an example we carry out the computations for a non-formal simply connected 7-manifold.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:18:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)Free loop spaces, Koszul duality and A-infinity algebras$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_18_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:18:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_18_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:18:j_idt1537:0:fullText"});}); Download (jpg)Omslagsframsida$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_18_j_idt1541_0_j_idt1544",{id:"formSmash:items:resultList:18:j_idt1541:0:j_idt1544",widgetVar:"widget_formSmash_items_resultList_18_j_idt1541_0_j_idt1544",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:18:j_idt1541:0:otherAttachment"});}); 20. Restricted Gerstenhaber algebra structure on the free loop homology of (S<sup>n</sup>×S<sup>n</sup>)<sup>#m</sup> Börjeson, Kaj PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt1274",{id:"formSmash:items:resultList:19:j_idt1274",widgetVar:"widget_formSmash_items_resultList_19_j_idt1274",onLabel:"Börjeson, Kaj ",offLabel:"Börjeson, Kaj ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Restricted Gerstenhaber algebra structure on the free loop homology of (S^{n}×S^{n})^{#m}Manuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:19:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_19_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We compute the 2-primary restricted Gerstenhaber algebra structure on the free loop homology of (S

^{n}×S^{n})^{#m}. To this end we construct a small complex with an explicit retract from the Hochschild cohomology complex of the cohomology algebra. The methods involved are Koszul duality, PBW-bases and the perturbation lemma.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:19:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 21. Gravity formality Campos, Ricardoet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt1277",{id:"formSmash:items:resultList:20:j_idt1277",widgetVar:"widget_formSmash_items_resultList_20_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ward, Benjamin C.Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Gravity formality2018Inngår i: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 331, s. 439-483Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:20:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_20_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We show that Willwacher's cyclic formality theorem can be extended to preserve natural Gravity operations on cyclic multivector fields and cyclic multidifferential operators. We express this in terms of a homotopy Gravity quasiisomorphism with explicit local formulas. For this, we develop operadic tools related to mixed complexes and cyclic homology and prove that the operad M(O )of natural operations on cyclic operators is formal and hence quasi-isomorphic to the Gravity operad.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:20:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 22. Monomials as Sums of <em>k-</em>th Powers of Forms Carlini, Enricoet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt1277",{id:"formSmash:items:resultList:21:j_idt1277",widgetVar:"widget_formSmash_items_resultList_21_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Oneto, AlessandroStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. Polytechnic University of Turin, Italy.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Monomials as Sums of*k-*th Powers of Forms2015Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 2, s. 650-658Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:21:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_21_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Motivated by recent results on the Waring problem for polynomial rings [4] and representation of monomial as sum of powers of linear forms [3], we consider the problem of presenting monomials of degree

*kd*as sums of*k*th-powers of forms of degree*d*. We produce a general bound on the number of summands for any number of variables which we refine in the two variables case. We completely solve the*k*= 3 case for monomials in two and three variables.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:21:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_21_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:21:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_21_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:21:j_idt1537:0:fullText"});}); 23. On ideals generated by two generic quadratic forms in the exterior algebra Crispin Quiñonez, Veronicaet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt1277",{id:"formSmash:items:resultList:22:j_idt1277",widgetVar:"widget_formSmash_items_resultList_22_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lundqvist, SamuelStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.Nenashev, GlebStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On ideals generated by two generic quadratic forms in the exterior algebraManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:22:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_22_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Based on the structure theory of pairs of skew-symmetric matrices, we give a conjecture for the Hilbert series of the exterior algebra modulo the ideal generated by two generic quadratic forms. We show that the conjectured series is an upper bound in the coefficient-wise sense, and we determine a majority of the coefficients. We also conjecture that the series is equal to the series of the squarefree polynomial ring modulo the ideal generated by the squares of two generic linear forms.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:22:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 24. A Proof and Formalization of the Initiality Conjecture of Dependent Type Theory de Boer, Menno PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt1274",{id:"formSmash:items:resultList:23:j_idt1274",widgetVar:"widget_formSmash_items_resultList_23_j_idt1274",onLabel:"de Boer, Menno ",offLabel:"de Boer, Menno ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Proof and Formalization of the Initiality Conjecture of Dependent Type Theory2020Licentiatavhandling, monografi (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:23:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_23_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this licentiate thesis we present a proof of the initiality conjecture for Martin-Löf’s type theory with

**0**,**1**,**N**, A**+**B**,**∏_{A}B**,**∑_{A}B_{,}**Id**_{A}(u,v), countable hierarchy of universes (**U**_{i})_{iєN}closed under these type constructors and with type of elements (**E****L**_{i}(a))_{iєN}. We employ the categorical semantics of contextual categories. The proof is based on a formalization in the proof assistant Agda done by Guillaume Brunerie and the author. This work was part of a joint project with Peter LeFanu Lumsdaine and Anders Mörtberg, who are developing a separate formalization of this conjecture with respect to categories with attributes and using the proof assistant Coq over the UniMath library instead. Results from this project are planned to be published in the future.We start by carefully setting up the syntax and rules for the dependent type theory in question followed by an introduction to contextual categories. We then define the partial interpretation of raw syntax into a contextual category and we prove that this interpretation is total on well-formed input. By doing so, we define a functor from the term model, which is built out of the syntax, into any contextual category and we show that any two such functors are equal. This establishes that the term model is initial among contextual categories. At the end we discuss details of the formalization and future directions for research. In particular, we discuss a memory issue that arose in type checking the formalization and how it was resolved.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:23:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_23_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:23:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_23_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:23:j_idt1537:0:fullText"});}); 25. Elevers skilda sätt att erfara talmönster - en studie av elever i årskurs 3 och 4 Ekdahl, Anna-Lena PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt1274",{id:"formSmash:items:resultList:24:j_idt1274",widgetVar:"widget_formSmash_items_resultList_24_j_idt1274",onLabel:"Ekdahl, Anna-Lena ",offLabel:"Ekdahl, Anna-Lena ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Institutionen för matematikämnets och naturvetenskapsämnenas didaktik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Elevers skilda sätt att erfara talmönster - en studie av elever i årskurs 3 och 42012Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgaveAbstract [sv] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:24:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_24_j_idt1312_0_j_idt1313",onLabel:"Abstract [sv]",offLabel:"Abstract [sv]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Matematiken handlar i mångt och mycket om att lösa problem och se mönster. Talmönster är en viktig del inom algebran och aritmetiken och är det fenomen som jag i denna studie vill undersöka elevers uppfattningar av. Syftet med föreliggande kvalitativa studie är att skapa kunskap om elevers skilda sätt att erfara talmönster, såväl talföljder som visuella talmönster. Därutöver syftar studien till att identifiera kritiska aspekter utifrån de skilda sätt som talmönstren erfars av eleverna.

Nio elever i årskurs 3 och 4 har intervjuats utifrån ett antal talmönster. Fenomenografin och variationsteorin utgör studiens teoretiska utgångspunkter och har använts för att analysera materialet. I analysen har förutom likheter och skillnader mellan sätten att erfara, innehållet i elevutsagorna analyserats utifrån erfarandets referentiella och strukturella aspekt.

Resultatet av den fenomenografiska analysen har utmynnat i följande sex beskrivningskategorier:

*Jämn förflyttning, Konstant eller icke-konstant skillnad, Kombination av delar, Relation mellan vissa delar, Olika del- och helhetsstrukturer och Utöver angiven helhet*. I analysen har de aspekter som eleverna fokuserat på varit vägledande för att skilja kategorierna åt och identifiera sex kritiska aspekter. En av dessa kritiska aspekter handlar om att urskilja att förhållandet mellan delarna i mönstret kan se olika ut. En annan kritisk aspekt är fråga om att kunna urskilja delarnas inbördes relation, relationernas förhållande till helheten och den icke angivna helheten. En tredje innebär att delarna behöver urskiljas samtidigt som helheten. Inte nödvändigtvis samtliga delar, men tillräckligt många för att se en regelbundenhet.Studiens resultat har gett didaktiska implikationer om vad eleverna i en undervisningssituation behöver ges möjlighet att urskilja för att utveckla ett mer innehållsrikt och differentierat sätt att erfara talmönster.

Resultatet diskuteras utifrån tidigare internationella undersökningar. Det förs även en diskussion om vad studiens resultat kan tillföra och de didaktiska implikationer resultatet ger.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:24:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)Talmönster årskurs 3och 4$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_24_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:24:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_24_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:24:j_idt1537:0:fullText"});}); 26. A category-theoretic version of the identity type weak factorization system Emmenegger, Jacopo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt1274",{id:"formSmash:items:resultList:25:j_idt1274",widgetVar:"widget_formSmash_items_resultList_25_j_idt1274",onLabel:"Emmenegger, Jacopo ",offLabel:"Emmenegger, Jacopo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A category-theoretic version of the identity type weak factorization systemManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:25:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_25_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Gambino and Garner proved that the syntactic category of a dependent type theory with identity types can be endowed with a weak factorization system structure, called identity type weak factorization system. In this paper we consider an enrichment of Joyal's notion of tribe which allow us to prove a purely category-theoretic version of the identity type weak factorization system, thus generalizing Gambino and Garner's result. We investigate then how it relates with other well-known weak factorization systems, namely those arising from Quillen model structures on the category of topological spaces and on the category of small groupoids.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:25:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_25_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:25:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_25_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:25:j_idt1537:0:fullText"});}); 27. Exact completion and type-theoretic structures Emmenegger, Jacopo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt1274",{id:"formSmash:items:resultList:26:j_idt1274",widgetVar:"widget_formSmash_items_resultList_26_j_idt1274",onLabel:"Emmenegger, Jacopo ",offLabel:"Emmenegger, Jacopo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Exact completion and type-theoretic structures2019Doktoravhandling, med artikler (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_26_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:26:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_26_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This thesis consists of four papers and is a contribution to the study of representations of extensional properties in intensional type theories using, mainly, the language and tools from category theory. Our main focus is on exact completions of categories with weak finite limits as a category-theoretic description of the setoid construction in Martin-Löf's intensional type theory.

Paper I, which is joint work with Erik Palmgren, provides sufficient conditions for such an exact completion to produce a model of the system CETCS (Constructive Elementary Theory of the Category of Sets), a finite axiomatisation of the theory of well-pointed locally cartesian closed pretoposes with a natural numbers object and enough projectives. In particular, we use a condition inspired by Aczel's set-theoretic Fullness Axiom to obtain the local cartesian closure of an exact completion. As an application, we obtain a simple uniform proof that the category of setoids is a model of CETCS.

Paper II was prompted by the discovery of an overlooked issue in the characterisationof local cartesian closure for exact completions due to Carboni and Rosolini. In this paper we clarify the problem, show that their characterisation is still valid when the base category has finite limits, and provide a complete solution in the general case of a category with weak finite limits.

In paper III we generalise the approach used in paper I to obtain the local cartesian closure of an exact completion to arbitrary categories with finite limits. We then show how this condition inspired by the Fullness Axiom naturally arises in several homotopy categories and apply this result to obtain the local cartesian closure of the exact completion of the homotopy category of spaces, thus answering a question left open by Marino Gran and Enrico Vitale.

Finally, in paper IV we abandon the pure category-theoretic approach and instead present a type-theoretic construction, formalised in Coq, of W-types in the category of setoids from dependent W-types in the underlying intensional theory. In particular, contrary to previous approaches, this construction does not require the assumption of Uniqueness of Identity Proofs nor recursion into a type universe.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:26:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)Exact completion and type-theoretic structures$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_26_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:26:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_26_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:26:j_idt1537:0:fullText"});}); Download (jpg)Omslagsframsida$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_26_j_idt1541_0_j_idt1544",{id:"formSmash:items:resultList:26:j_idt1541:0:j_idt1544",widgetVar:"widget_formSmash_items_resultList_26_j_idt1541_0_j_idt1544",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:26:j_idt1541:0:otherAttachment"});}); 28. On the local cartesian closure of exact completions Emmenegger, Jacopo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt1274",{id:"formSmash:items:resultList:27:j_idt1274",widgetVar:"widget_formSmash_items_resultList_27_j_idt1274",onLabel:"Emmenegger, Jacopo ",offLabel:"Emmenegger, Jacopo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On the local cartesian closure of exact completionsManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:27:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_27_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); A characterisation of cartesian closure of exact completions as a property of the projective objects was given by Carboni and Rosolini. We show that the argument used to prove that characterisation is equivalent to the projectives being closed under binary products (equivalently, being internally projective). The property in question is the existence of weak simple products (a slight strengthening of weak exponentials) and the argument used relies on two claims: that weak simple products endow the internal logic with universal quantification, and that an exponential is the quotient of a weak exponential. We show that either these claims hold if and only if the projectives are internally projectives, which entails that Carboni and Rosolini's characterisation only applies to ex/lex completions. We then argue that this limitation depends on the universal property of weak simple products, and derive from this observation an alternative notion, which we call generalised weak simple product. We conclude by showing that existence of generalised weak simple products in the subcategory of projectives is equivalent to the cartesian closure of the exact category, thus obtaining a complete characterisation of (local) cartesian closure for exact completions of categories with weak finite limits.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:27:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_27_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:27:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_27_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:27:j_idt1537:0:fullText"});}); 29. The Fullness Axiom and exact completions of homotopy categories Emmenegger, Jacopo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt1274",{id:"formSmash:items:resultList:28:j_idt1274",widgetVar:"widget_formSmash_items_resultList_28_j_idt1274",onLabel:"Emmenegger, Jacopo ",offLabel:"Emmenegger, Jacopo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The Fullness Axiom and exact completions of homotopy categoriesManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:28:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_28_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We use a category-theoretic formulation of Aczel's Fullness Axiom from Constructive Set Theory to derive the local cartesian closure of an exact completion. As an application, we prove that such a formulation is valid in the homotopy category of any model category satisfying mild requirements, thus obtaining in particular the local cartesian closure of the exact completion of topological spaces and homotopy classes of maps. Under a type-theoretic reading, these results provide a general motivation for the local cartesian closure of the category of setoids. However, results and proofs are formulated solely in the language of categories, and no knowledge of type theory or constructive set theory is required on the reader's part.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:28:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_28_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:28:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_28_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:28:j_idt1537:0:fullText"});}); 30. W-types in setoids Emmenegger, Jacopo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt1274",{id:"formSmash:items:resultList:29:j_idt1274",widgetVar:"widget_formSmash_items_resultList_29_j_idt1274",onLabel:"Emmenegger, Jacopo ",offLabel:"Emmenegger, Jacopo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); W-types in setoidsManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:29:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_29_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); W-types and their categorical analogue, initial algebras for polynomial endofunctors, are an important tool in predicative systems to replace transfinite recursion on well-orderings. Current arguments to obtain W-types in quotient completions rely on assumptions, like Uniqueness of Identity Proofs, or on constructions that involve recursion into a universe, that limit their applicability to a specific setting. We present an argument, verified in Coq, that instead uses dependent W-types in the underlying type theory to construct W-types in the setoid model. The immediate advantage is to have a proof more type-theoretic in flavour, which directly uses recursion on the underlying W-type to prove initiality. Furthermore, taking place in intensional type theory and not requiring any recursion into a universe, it may be generalised to various categorical quotient completions, with the aim of finding a uniform construction of extensional W-types.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:29:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_29_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:29:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_29_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:29:j_idt1537:0:fullText"});}); 31. Exact completion and constructive theories of sets Emmenegger, Jacopo PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt1274",{id:"formSmash:items:resultList:30:j_idt1274",widgetVar:"widget_formSmash_items_resultList_30_j_idt1274",onLabel:"Emmenegger, Jacopo ",offLabel:"Emmenegger, Jacopo ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt1277",{id:"formSmash:items:resultList:30:j_idt1277",widgetVar:"widget_formSmash_items_resultList_30_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Palmgren, ErikStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Exact completion and constructive theories of setsManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:30:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_30_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In the present paper we use the theory of exact completions to study categorical properties of small setoids in Martin-Loef type theory and, more generally, of models of the Constructive Elementary Theory of the Category of Sets, in terms of properties of their subcategories of choice objects (i.e. objects satisfying the axiom of choice). Because of these intended applications, we deal with categories that lack equalisers and just have weak ones, but whose objects can be regarded as collections of global elements. In this context, we study the internal logic of the categories involved, and employ this analysis to give a sufficient condition for the local cartesian closure of an exact completion. Finally, we apply this result to show when an exact completion produces a model of CETCS.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:30:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_30_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:30:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_30_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:30:j_idt1537:0:fullText"});}); 32. Differential operators on some classes of rings Eriksson, Anders PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt1274",{id:"formSmash:items:resultList:31:j_idt1274",widgetVar:"widget_formSmash_items_resultList_31_j_idt1274",onLabel:"Eriksson, Anders ",offLabel:"Eriksson, Anders ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Differential operators on some classes of rings2000Doktoravhandling, med artikler (Annet vitenskapelig)33. A short proof of Glivenko theorems for intermediate predicate logics Espíndola, Christian PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt1274",{id:"formSmash:items:resultList:32:j_idt1274",widgetVar:"widget_formSmash_items_resultList_32_j_idt1274",onLabel:"Espíndola, Christian ",offLabel:"Espíndola, Christian ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A short proof of Glivenko theorems for intermediate predicate logics2013Inngår i: Archive for mathematical logic, ISSN 0933-5846, E-ISSN 1432-0665, Vol. 52, nr 7-8, s. 823-826Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:32:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_32_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We give a simple proof-theoretic argument showing that Glivenko’s theorem for propositional logic and its version for predicate logic follow as an easy consequence of the deduction theorem, which also proves some Glivenko type theorems relating intermediate predicate logics between intuitionistic and classical logic. We consider two schemata, the double negation shift (

*DNS*) and the one consisting of instances of the principle of excluded middle for sentences (*REM*). We prove that both schemata combined derive classical logic, while each one of them provides a strictly weaker intermediate logic, and neither of them is derivable from the other. We show that over every intermediate logic there exists a maximal intermediate logic for which Glivenko’s theorem holds. We deduce as well a characterization of*DNS*, as the weakest (with respect to derivability) scheme that added to*REM*derives classical logic.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:32:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)Fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_32_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:32:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_32_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:32:j_idt1537:0:fullText"});}); 34. Achieving completeness: from constructive set theory to large cardinals Espíndola, Christian PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt1274",{id:"formSmash:items:resultList:33:j_idt1274",widgetVar:"widget_formSmash_items_resultList_33_j_idt1274",onLabel:"Espíndola, Christian ",offLabel:"Espíndola, Christian ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Achieving completeness: from constructive set theory to large cardinals2016Doktoravhandling, monografi (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:33:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_33_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This thesis is an exploration of several completeness phenomena, both in the constructive and the classical settings. After some introductory chapters in the first part of the thesis where we outline the background used later on, the constructive part contains a categorical formulation of several constructive completeness theorems available in the literature, but presented here in an unified framework. We develop them within a constructive reverse mathematical viewpoint, highlighting the metatheory used in each case and the strength of the corresponding completeness theorems.

The classical part of the thesis focuses on infinitary intuitionistic propositional and predicate logic. We consider a propositional axiomatic system with a special distributivity rule that is enough to prove a completeness theorem, and we introduce weakly compact cardinals as the adequate metatheoretical assumption for this development. Finally, we return to the categorical formulation focusing this time on infinitary first-order intuitionistic logic. We propose a first-order system with a special rule, transfinite transitivity, that embodies both distributivity as well as a form of dependent choice, and study the extent to which completeness theorems can be established. We prove completeness using a weakly compact cardinal, and, like in the constructive part, we study disjunction-free fragments as well. The assumption of weak compactness is shown to be essential for the completeness theorems to hold.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:33:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)Achieving completeness: from constructive set theory to large cardinals$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_33_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:33:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_33_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:33:j_idt1537:0:fullText"});}); Download (jpg)presentationsbild$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_33_j_idt1541_0_j_idt1544",{id:"formSmash:items:resultList:33:j_idt1541:0:j_idt1544",widgetVar:"widget_formSmash_items_resultList_33_j_idt1541_0_j_idt1544",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:33:j_idt1541:0:otherAttachment"});}); 35. Semantic Completeness of First-Order Theories in Constructive Reverse Mathematics Espíndola, Christian PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt1274",{id:"formSmash:items:resultList:34:j_idt1274",widgetVar:"widget_formSmash_items_resultList_34_j_idt1274",onLabel:"Espíndola, Christian ",offLabel:"Espíndola, Christian ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Semantic Completeness of First-Order Theories in Constructive Reverse Mathematics2016Inngår i: Notre Dame Journal of Formal Logic, ISSN 0029-4527, E-ISSN 1939-0726, Vol. 57, nr 2, s. 281-286Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:34:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_34_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We introduce a general notion of semantic structure for first-order theories, covering a variety of constructions such as Tarski and Kripke semantics, and prove that, over Zermelo–Fraenkel set theory (ZF), the completeness of such semantics is equivalent to the Boolean prime ideal theorem (BPI). Using a result of McCarty (2008), we conclude that the completeness of Kripke semantics is equivalent, over intuitionistic Zermelo–Fraenkel set theory (IZF), to the Law of Excluded Middle plus BPI. Along the way, we also prove the equivalence, over ZF, between BPI and the completeness theorem for Kripke semantics for both first-order and propositional theories.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:34:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 36. Free Lunch for Optimisation under the Universal Distribution Everitt, Tom PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt1274",{id:"formSmash:items:resultList:35:j_idt1274",widgetVar:"widget_formSmash_items_resultList_35_j_idt1274",onLabel:"Everitt, Tom ",offLabel:"Everitt, Tom ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt1277",{id:"formSmash:items:resultList:35:j_idt1277",widgetVar:"widget_formSmash_items_resultList_35_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lattimore, TorHutter, MarcusPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Free Lunch for Optimisation under the Universal Distribution2014Inngår i: 2014 IEEE Congress on Evolutionary Computation (CEC), New York: IEEE Computer Society, 2014, s. 167-174Konferansepaper (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:35:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_35_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Function optimisation is a major challenge in computer science. The No Free Lunch theorems state that if all functions with the same histogram are assumed to be equally probable then no algorithm outperforms any other in expectation. We argue against the uniform assumption and suggest a universal prior exists for which there is a free lunch, but where no particular class of functions is favoured over another. We also prove upper and lower boundson the size of the free lunch.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:35:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 37. Constructive reflection principles for regular theories Forssell, Henrik PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt1274",{id:"formSmash:items:resultList:36:j_idt1274",widgetVar:"widget_formSmash_items_resultList_36_j_idt1274",onLabel:"Forssell, Henrik ",offLabel:"Forssell, Henrik ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt1277",{id:"formSmash:items:resultList:36:j_idt1277",widgetVar:"widget_formSmash_items_resultList_36_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen. University of Oslo.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lumsdaine, Peter LeFanuStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Constructive reflection principles for regular theoriesManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:36:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_36_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Classically, any structure for a signature Σ may be completed to a model of a desired regular theory T by means of the chase construction or small object argument. Moreover, this exhibits Mod(T) as weakly reflective in Str(Σ).

We investigate this in the constructive setting. The basic construction is unproblematic, however, it is no longer a weak reflection. Indeed, we show that various reflection principles for models of regular theories are equivalent to choice principles in the ambient set theory. However, the embedding of a structure into its chase-completion still satisfies a conservativity property, which suffices for applications such as the completeness of regular logic with respect to Tarski (i.e. set) models.

Unlike most constructive developments of predicate logic, we do not assume that equality between symbols in the signature is decidable. While in this setting, we also give a version of one classical lemma which is trivial over discrete signatures but more interesting here: the abstraction of constants in a proof to variables.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:36:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 38. Type Theoretical Databases Forssell, Henrik PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt1274",{id:"formSmash:items:resultList:37:j_idt1274",widgetVar:"widget_formSmash_items_resultList_37_j_idt1274",onLabel:"Forssell, Henrik ",offLabel:"Forssell, Henrik ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt1277",{id:"formSmash:items:resultList:37:j_idt1277",widgetVar:"widget_formSmash_items_resultList_37_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Robbestad Gylterud, HåkonStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.Spivak, David I.Massachusetts Institute of Technology, USA.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Type Theoretical DatabasesManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:37:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_37_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to represent tables in a natural way. Thus the category is a model for databases, a single mathematical structure in which all database schemas and instances (of a suitable, but sufficiently general form) are represented. The type theory then allows for the specification of database schemas and instances, the manipulation of the same with the usual type-theoretic operations, and the posing of queries.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:37:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 39. Big Brother Logic Gasquet, Olivieret al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt1277",{id:"formSmash:items:resultList:38:j_idt1277",widgetVar:"widget_formSmash_items_resultList_38_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Goranko, ValentinStockholms universitet, Humanistiska fakulteten, Filosofiska institutionen. University of Johannesburg, South Africa.Schwarzentruber, FrançoisPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Big Brother Logic: visual-epistemic reasoning in stationary multi-agent systems2016Inngår i: Autonomous Agents and Multi-Agent Systems, ISSN 1387-2532, E-ISSN 1573-7454, Vol. 30, nr 5, s. 793-825Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:38:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_38_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider multi-agent scenarios where each agent controls a surveillance camera in the plane, with fixed position and angle of vision, but rotating freely. The agents can thus observe the surroundings and each other. They can also reason about each other’s observation abilities and knowledge derived from these observations. We introduce suitable logical languages for reasoning about such scenarios which involve atomic formulae stating what agents can see, multi-agent epistemic operators for individual, distributed and common knowledge, as well as dynamic operators reflecting the ability of cameras to turn around in order to reach positions satisfying formulae in the language. We also consider effects of public announcements. We introduce several different but equivalent versions of the semantics for these languages, discuss their expressiveness and provide translations in PDL style. Using these translations we develop algorithms and obtain complexity results for model checking and satisfiability testing for the basic logic BBL that we introduce here and for some of its extensions. Notably, we show that even for the extension with common knowledge, model checking and satisfiability testing remain in PSPACE. We also discuss the sensitivity of the set of validities to the admissible angles of vision of the agents’ cameras. Finally, we discuss some further extensions: adding obstacles, positioning the cameras in 3D or enabling them to change positions. Our work has potential applications to automated reasoning, formal specification and verification of observational abilities and knowledge of multi-robot systems.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:38:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 40. Logic as a Tool Goranko, Valentin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt1274",{id:"formSmash:items:resultList:39:j_idt1274",widgetVar:"widget_formSmash_items_resultList_39_j_idt1274",onLabel:"Goranko, Valentin ",offLabel:"Goranko, Valentin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Humanistiska fakulteten, Filosofiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Logic as a Tool: A Guide to Formal Logical Reasoning2016Bok (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:39:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_39_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The book explains the grammar, semantics and use of classical logical languages and teaches the reader how grasp the meaning and translate them to and from natural language. It illustrates with extensive examples the use of the most popular deductive systems -- axiomatic systems, semantic tableaux, natural deduction, and resolution -- for formalising and automating logical reasoning both on propositional and on first-order level, and provides the reader with technical skills needed for practical derivations in them. Systematic guidelines are offered on how to perform logically correct and well-structured reasoning using these deductive systems and the reasoning techniques that they employ.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:39:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 41. Temporal Logic Goranko, Valentin PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt1274",{id:"formSmash:items:resultList:40:j_idt1274",widgetVar:"widget_formSmash_items_resultList_40_j_idt1274",onLabel:"Goranko, Valentin ",offLabel:"Goranko, Valentin ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt1277",{id:"formSmash:items:resultList:40:j_idt1277",widgetVar:"widget_formSmash_items_resultList_40_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Humanistiska fakulteten, Filosofiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Galton, AntonyPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Temporal Logic2015Inngår i: Stanford Encyclopedia of Philosophy, ISSN 1095-5054, E-ISSN 1095-5054Artikkel i tidsskrift (Fagfellevurdert)42. Finite unions of submodules Gottlieb, Christian PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt1274",{id:"formSmash:items:resultList:41:j_idt1274",widgetVar:"widget_formSmash_items_resultList_41_j_idt1274",onLabel:"Gottlieb, Christian ",offLabel:"Gottlieb, Christian ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Finite unions of submodules2015Inngår i: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 43, nr 2, s. 847-855Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:41:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_41_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper is concerned with finite unions of ideals and modules. The first main result is that, if

*N*⊆*N*_{1}∪*N*_{2}∪ … ∪*N*_{s }is a covering of a module*N*by submodules*N*_{i }, such that all but two of the*N*_{i }are intersections of strongly irreducible modules, then*N*⊆*N*_{k }for some*k*. The special case when*N*is a multiplication module is considered. The second main result generalizes earlier results on coverings by primary submodules. In the last section unions of cosets is studied.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:41:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)Finite unions of submodules$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_41_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:41:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_41_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:41:j_idt1537:0:fullText"});}); 43. A Model-Theoretic Proof of Gödel's Theorem Granberg Olsson, Mattias PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt1274",{id:"formSmash:items:resultList:42:j_idt1274",widgetVar:"widget_formSmash_items_resultList_42_j_idt1274",onLabel:"Granberg Olsson, Mattias ",offLabel:"Granberg Olsson, Mattias ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Model-Theoretic Proof of Gödel's Theorem: Kripke's Notion of Fulfilment2017Independent thesis Advanced level (degree of Master (Two Years)), 20 poäng / 30 hpOppgaveAbstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:42:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_42_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The notion of fulfilment of a formula by a sequence of numbers, an approximation of truth due to Kripke, is presented and subsequently formalised in the weak arithmetic theory IΣ

_{1}, in some detail. After a number of technical results connecting the formalised notion to the meta-theoretical one a version of Gödel’s Incompleteness Theorem, that no consistent, recursively axiomatisable, Σ_{2}-sound extension*T*of Peano arithmetic is complete, is shown by construction of a true Π_{2}-sentence and a model of*T*where it is false, yielding its independence from*T*. These results are then generalised to a more general notion of fulfilment, proving that IΣ_{1}has no complete, consistent, recursively axiomatisable, Σ_{2}-sound extensions by a similar construction of an independent sentence. This generalisation comes at the cost of some naturality, however, and an explicit falsifying model will only be obtained under additional assumptions.The aim of the thesis is to reproduce in some detail the notions and results developed by Kripke and Quinsey and presented by Quinsey and Putnam. In particular no novel results are obtained.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:42:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_42_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:42:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_42_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:42:j_idt1537:0:fullText"});}); 44. Syzygies of Veronese Modules Greco, Ornellaet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt1277",{id:"formSmash:items:resultList:43:j_idt1277",widgetVar:"widget_formSmash_items_resultList_43_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Martino, IvanStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Syzygies of Veronese ModulesManuskript (preprint) (Annet vitenskapelig)45. Annals of Pure and Applied Logic Hirvonen, Åsaet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt1277",{id:"formSmash:items:resultList:44:j_idt1277",widgetVar:"widget_formSmash_items_resultList_44_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Väänänen, JoukoScanlon, ThomasWesterståhl, DagStockholms universitet, Humanistiska fakulteten, Filosofiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Annals of Pure and Applied Logic: Special Issue: Logic Colloquium 20152018Konferanseproceedings (Fagfellevurdert)46. A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory Hou, Kuen-Bang (Favonia)et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt1277",{id:"formSmash:items:resultList:45:j_idt1277",widgetVar:"widget_formSmash_items_resultList_45_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Finster, EricLicata, Daniel R.Lumsdaine, Peter LeFanuStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A mechanization of the Blakers-Massey connectivity theorem in Homotopy Type Theory2016Inngår i: LICS '16 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, New York, USA: Association for Computing Machinery (ACM), 2016, s. 565-574Konferansepaper (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:45:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_45_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper continues investigations in “synthetic homotopy theory”: the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory.

We present a mechanized proof of the Blakers-Massey connectivity theorem, a result relating the higher-dimensional homotopy groups of a pushout type (roughly, a space constructed by gluing two spaces along a shared subspace) to those of the components of the pushout. This theorem gives important information about the pushout type, and has a number of useful corollaries, including the Freudenthal suspension theorem, which has been studied in previous formalizations.

The new proof is more elementary than existing ones in abstract homotopy-theoretic settings, and the mechanization is concise and high-level, thanks to novel combinations of ideas from homotopy theory and type theory.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:45:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 47. A logic for temporal conditionals and a solution to the Sea Battle Puzzle Ju, Fengkuiet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt1277",{id:"formSmash:items:resultList:46:j_idt1277",widgetVar:"widget_formSmash_items_resultList_46_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Grilletti, GianlucaGoranko, ValentinStockholms universitet, Humanistiska fakulteten, Filosofiska institutionen. University of Johannesburg, South Africa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A logic for temporal conditionals and a solution to the Sea Battle Puzzle2018Inngår i: Advances in Modal Logic / [ed] Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer, London: College Publications, 2018, s. 379-398Konferansepaper (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:46:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_46_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle’s famous “Sea Battle Tomorrow” puzzle leads to a fatalistic conclusion: whether there will be a sea battle tomorrow or not, but that is necessarily the case now. We propose a branching-time logic LTC to formalise reasoning about temporal conditionals and provide that logic with adequate formal semantics. The logic LTC extends the Nexttime fragment of CTL∗ , with operators for model updates, restricting the domain to only future moments where antecedent is still possible to satisfy. We provide formal semantics for these operators that implements the restrictor interpretation of antecedents of temporalized conditionals, by suitably restricting the domain of discourse. As a motivating example, we demonstrate that a naturally formalised in our logic version of the ‘Sea Battle’ argument renders it unsound, thereby providing a solution to the problem with fatalist conclusion that it entails, because its underlying reasoning per cases argument no longer applies when these cases are treated not as material implications but as temporal conditionals. On the technical side, we analyze the semantics of LTC and provide a series of reductions of LTC-formulae, first recursively eliminating the dynamic update operators and then the path quantifiers in such formulae. Using these reductions we obtain a sound and complete axiomatization for LTC, and reduce its decision problem to that of the modal logic KD.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:46:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_46_j_idt1537_0_j_idt1540",{id:"formSmash:items:resultList:46:j_idt1537:0:j_idt1540",widgetVar:"widget_formSmash_items_resultList_46_j_idt1537_0_j_idt1540",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:46:j_idt1537:0:fullText"});}); 48. A Logic for Temporal Conditionals and a Solution to the Sea Battle Puzzle Ju, Fengkuiet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt1277",{id:"formSmash:items:resultList:47:j_idt1277",widgetVar:"widget_formSmash_items_resultList_47_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Grilletti, GianlucaGoranko, ValtentinStockholms universitet, Humanistiska fakulteten, Filosofiska institutionen. University of Johannesburg, South Africa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); A Logic for Temporal Conditionals and a Solution to the Sea Battle Puzzle2018Inngår i: Proceedings of the 12th International Conference on Advances in Modal Logic (AiML'2018) / [ed] Guram Bezhanishvili, Giovanna D'Agostino, George Metcalfe, Thomas Studer, College Publications, 2018, s. 407-426Konferansepaper (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:47:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_47_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Temporal reasoning with conditionals is more complex than both classical temporal reasoning and reasoning with timeless conditionals, and can lead to some rather counter-intuitive conclusions. For instance, Aristotle’s famous “Sea Battle Tomorrow” puzzle leads to a fatalistic conclusion: whether there will be a sea battle tomorrow or not, but that is necessarily the case now. We propose a branching-time logic LTC to formalise reasoning about temporal conditionals and provide that logic with adequate formal semantics. The logic LTC extends the Nexttime fragment of CTL∗ , with operators for model updates, restricting the domain to only future moments where antecedent is still possible to satisfy. We provide formal semantics for these operators that implements the restrictor interpretation of antecedents of temporalized conditionals, by suitably restricting the domain of discourse. As a motivating example, we demonstrate that a naturally formalised in our logic version of the ‘Sea Battle’ argument renders it unsound, thereby providing a solution to the problem with fatalist conclusion that it entails, because its underlying reasoning per cases argument no longer applies when these cases are treated not as material implications but as temporal conditionals. On the technical side, we analyze the semantics of LTC and provide a series of reductions of LTC-formulae, first recursively eliminating the dynamic update operators and then the path quantifiers in such formulae. Using these reductions we obtain a sound and complete axiomatization for LTC, and reduce its decision problem to that of the modal logic KD.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:47:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 49. The homotopy theory of type theories Kapulkin, Chris PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt1274",{id:"formSmash:items:resultList:48:j_idt1274",widgetVar:"widget_formSmash_items_resultList_48_j_idt1274",onLabel:"Kapulkin, Chris ",offLabel:"Kapulkin, Chris ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt1277",{id:"formSmash:items:resultList:48:j_idt1277",widgetVar:"widget_formSmash_items_resultList_48_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Western Ontario.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lumsdaine, Peter LeFanuStockholms universitet, Naturvetenskapliga fakulteten, Matematiska institutionen.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The homotopy theory of type theoriesManuskript (preprint) (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:48:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_48_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We construct a left semi-model structure on the category of intensional type theories (precisely, on CxlCat_{Id,1,Σ(,Πext)}). This presents an infinity-category of such type theories; we show moreover that there is an infinity-functor Cl_∞ from there to the infinity-category of suitably structured quasi-categories. This allows a precise formulation of the conjectures that intensional type theory gives internal languages for higher categories, and provides a framework and toolbox for further progress on these conjectures.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:48:j_idt1312:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 50. D-module and F-module length of local cohomology modules Katzman, Mordechaiet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt1277",{id:"formSmash:items:resultList:49:j_idt1277",widgetVar:"widget_formSmash_items_resultList_49_j_idt1277",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ma, LinquanSmirnov, IlyaUniversity of Michigan, USA.Zhang, WenliangPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); D-module and F-module length of local cohomology modules2018Inngår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, nr 12, s. 8551-8580Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt1312_0_j_idt1313",{id:"formSmash:items:resultList:49:j_idt1312:0:j_idt1313",widgetVar:"widget_formSmash_items_resultList_49_j_idt1312_0_j_idt1313",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Let R be a polynomial or power series ring over a field k. We study the length of local cohomology modules H-I(j) (R) in the category of D-modules and F-modules. We show that the D-module length of H-I(j) (R) is bounded by a polynomial in the degree of the generators of I. In characteristic p > 0 we obtain upper and lower bounds on the F-module length in terms of the dimensions of Frobenius stable parts and the number of special primes of local cohomology modules of R/I. The obtained upper bound is sharp if R/I is an isolated singularity, and the lower bound is sharp when R/I is Gorenstein and F-pure. We also give an example of a local cohomology module that has different D-module and F-module lengths.

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