Semantic Completeness of First-Order Theories in Constructive Reverse 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
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.
completeness, constructive reverse mathematics, Kripke semantics, algebraic semantics
Algebra and Logic
Research subject Mathematical Logic
IdentifiersURN: urn:nbn:se:su:diva-130536DOI: 10.1215/00294527-3470433ISI: 000378164700008OAI: oai:DiVA.org:su-130536DiVA: diva2:930784