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Semantic Completeness of First-Order Theories in Constructive Reverse Mathematics
Stockholm University, Faculty of Science, Department of Mathematics.
2016 (English)In: Notre Dame Journal of Formal Logic, ISSN 0029-4527, E-ISSN 1939-0726, Vol. 57, no 2, 281-286 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2016. Vol. 57, no 2, 281-286 p.
Keyword [en]
completeness, constructive reverse mathematics, Kripke semantics, algebraic semantics
National Category
Algebra and Logic
Research subject
Mathematical Logic
Identifiers
URN: urn:nbn:se:su:diva-130536DOI: 10.1215/00294527-3470433ISI: 000378164700008OAI: oai:DiVA.org:su-130536DiVA: diva2:930784
Available from: 2016-05-25 Created: 2016-05-25 Last updated: 2016-08-08Bibliographically approved

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Espíndola, Christian
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