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Interpretability over peano arithmetic

Published online by Cambridge University Press:  12 March 2014

Claes Strannegård
Claes Strannegård*
Affiliation:
Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 Cs Utrecht, The Netherlands, E-mail: [email protected]
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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 ILMω. 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).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 4 , December 1999 , pp. 1407 - 1425
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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