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Finite Kripke Models and Predicate Logics of Provability

Sergei Artemov and Giorgie Dzhaparidze
The Journal of Symbolic Logic
Vol. 55, No. 3 (Sep., 1990), pp. 1090-1098
DOI: 10.2307/2274475
Stable URL: http://www.jstor.org/stable/2274475
Page Count: 9
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Finite Kripke Models and Predicate Logics of Provability
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Abstract

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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