Finite Kripke models and predicate logics of provability

Journal of Symbolic Logic 55 (3):1090-1098 (1990)
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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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Sergei Artemov
CUNY Graduate Center

Citations of this work

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Fixed-point properties for predicate modal logics.Sohei Iwata & Taishi Kurahashi - 2020 - Annals of the Japan Association for Philosophy of Science 29:1-25.

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References found in this work

The predicate modal logic of provability.Franco Montagna - 1984 - Notre Dame Journal of Formal Logic 25 (2):179-189.
The Unprovability of Consistency. An Essay in Modal Logic.C. Smoryński - 1979 - Journal of Symbolic Logic 46 (4):871-873.

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