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Parametricity, automorphisms of the universe, and excluded middle
University of Birmingham.
University of Birmingham.
Stockholm University, Faculty of Science, Department of Mathematics. (Logik)ORCID iD: 0000-0003-1390-2970
University of San Diego.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

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.

National Category
Algebra and Logic
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:su:diva-140146OAI: oai:DiVA.org:su-140146DiVA: diva2:1077739
Note

Submitted

Available from: 2017-02-28 Created: 2017-02-28 Last updated: 2017-02-28

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
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  • modern-language-association-8th-edition
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