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Submodels of Kripke Models

By A. Visser

Abstract

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

Topics: Wijsbegeerte, Kripke models, Intuitionistic Logic, Heyting Arithmetic
Year: 1998
OAI identifier: oai:dspace.library.uu.nl:1874/26906
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