Journal of Symbolic Logic

Finite Kripke Models and Predicate Logics of Provability

Sergei Artemov and Giorgie Dzhaparidze

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The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic: If a closed modal predicate-logical formula $R$ is not valid in some finite Kripke model, then there exists an arithmetical interpretation $f$ such that $PA \nvdash fR$. This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of $QGL$ and $QS$). The proof was obtained by adding "the predicate part" as a specific addition to the standard Solovay construction.

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J. Symbolic Logic, Volume 55, Issue 3 (1990), 1090-1098.

First available in Project Euclid: 6 July 2007

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Artemov, Sergei; Dzhaparidze, Giorgie. Finite Kripke Models and Predicate Logics of Provability. J. Symbolic Logic 55 (1990), no. 3, 1090--1098.

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