## Journal of Symbolic Logic

### Interpretability Over Peano Arithmetic

Claes Strannegard

#### Abstract

We investigate the modal logic of interpretability over Peano arithmetic. Our main result is a compactness theorem that extends the arithmetical completeness theorem for the interpretability logic ILM$^\omega$. This extension concerns recursively enumerable sets of formulas of interpretability logic (rather than single formulas). As corollaries we obtain a uniform arithmetical completeness theorem for the interpretability logic ILM and a partial answer to a question of Orey from 1961. After some simplifications, we also obtain Shavrukov's embedding theorem for Magari algebras (a.k.a. diagonalizable algebras).

#### Article information

Source
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1407-1425.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745928

Mathematical Reviews number (MathSciNet)
MR1780061

Zentralblatt MATH identifier
0945.03027

JSTOR