Interpretability over peano arithmetic

Journal of Symbolic Logic 64 (4):1407-1425 (1999)
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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 ω . 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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References found in this work

Relative Interpretations.Steven Orey - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (7-10):146-153.
Relative Interpretations.Steven Orey - 1961 - Mathematical Logic Quarterly 7 (7‐10):146-153.
A Note on the Diagonalizable Algebras of PA and ZF.V. Yu Shavrukov - 1993 - Annals of Pure and Applied Logic 61 (1-2):161-173.

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