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Finite Kripke models and predicate logics of provability

Published online by Cambridge University Press:  12 March 2014

Sergei Artemov  and
Giorgie Dzhaparidze
Sergei Artemov
Affiliation:
Steklov Mathematical Institute, Academy of Sciences of the USSR, 117966 Moscow, USSR
Giorgie Dzhaparidze
Affiliation:
Institute of Philosophy, Academy of Sciences of the Georgian SSR, 380009 Tbilisi, USSR
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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 ⊬ 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 55 , Issue 3 , September 1990 , pp. 1090 - 1098
Copyright
Copyright © Association for Symbolic Logic 1990

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References

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