Journal of Symbolic Logic
- J. Symbolic Logic
- Volume 64, Issue 4 (1999), 1407-1425.
Interpretability Over Peano Arithmetic
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).
J. Symbolic Logic, Volume 64, Issue 4 (1999), 1407-1425.
First available in Project Euclid: 6 July 2007
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Strannegard, Claes. Interpretability Over Peano Arithmetic. J. Symbolic Logic 64 (1999), no. 4, 1407--1425. https://projecteuclid.org/euclid.jsl/1183745928