Submodels of Kripke models

Archive for Mathematical Logic 40 (4):277-295 (2001)
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Abstract

A Kripke model ? is a submodel of another Kripke model ℳ if ? is obtained by restricting the set of nodes of ℳ. In this paper we show that the class of formulas of Intuitionistic Predicate Logic that is preserved under taking submodels of Kripke models is precisely the class of semipositive formulas. This result is an analogue of the Łoś-Tarski theorem for the Classical Predicate Calculus.In Appendix A we prove that for theories with decidable identity we can take as the embeddings between domains in Kripke models of the theory, the identical embeddings. This is a well known fact, but we know of no correct proof in the literature. In Appendix B we answer, negatively, a question posed by Sam Buss: whether there is a classical theory T, such that ℋT is HA. Here ℋT is the theory of all Kripke models ℳ such that the structures assigned to the nodes of ℳ all satisfy T in the sense of classical model theory

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Citations of this work

Syntactic Preservation Theorems for Intuitionistic Predicate Logic.Jonathan Fleischmann - 2010 - Notre Dame Journal of Formal Logic 51 (2):225-245.
Preservation Theorems for Kripke Models.Morteza Moniri & Mostafa Zaare - 2009 - Mathematical Logic Quarterly 55 (2):177-184.
Back and Forth Between First-Order Kripke Models.Tomasz Połacik - 2008 - Logic Journal of the IGPL 16 (4):335-355.
Extensions of Kripke Models.Mostafa Zaare - 2017 - Logic Journal of the IGPL 25 (5):697-699.

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