Journal of Symbolic Logic

Interpretability Over Peano Arithmetic

Claes Strannegard

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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).

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

First available in Project Euclid: 6 July 2007

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Strannegard, Claes. Interpretability Over Peano Arithmetic. J. Symbolic Logic 64 (1999), no. 4, 1407--1425.

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