## Journal of Symbolic Logic

### Finite Kripke Models and Predicate Logics of Provability

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743407

Mathematical Reviews number (MathSciNet)
MR1071316

Zentralblatt MATH identifier
0723.03006

JSTOR