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

Liar-Type Paradoxes and the Incompleteness Phenomena.Makoto Kikuchi & Taishi Kurahashi - 2016 - Journal of Philosophical Logic 45 (4):381-398.
Fixed-Point Properties for Predicate Modal Logics.Sohei Iwata & Taishi Kurahashi - 2020 - Annals of the Japan Association for Philosophy of Science 29:1-25.
An Arithmetically Complete Predicate Modal Logic.Yunge Hao & George Tourlakis - 2021 - Bulletin of the Section of Logic 50 (4):513-541.

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References found in this work

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

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