Arithmetical Completeness Theorem for Modal Logic $$mathsf{}$$

Studia Logica 106 (2):219-235 (2018)
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Abstract

We prove that for any recursively axiomatized consistent extension T of Peano Arithmetic, there exists a \ provability predicate of T whose provability logic is precisely the modal logic \. For this purpose, we introduce a new bimodal logic \, and prove the Kripke completeness theorem and the uniform arithmetical completeness theorem for \.

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References found in this work

The Logic of Provability.George Boolos - 1993 - Cambridge and New York: Cambridge University Press.
Provability Interpretations of Modal Logic.Robert M. Solovay - 1981 - Journal of Symbolic Logic 46 (3):661-662.
Four valued semantics and the liar.Albert Visser - 1984 - Journal of Philosophical Logic 13 (2):181 - 212.
The Logic of Provability.Philip Scowcroft - 1995 - Philosophical Review 104 (4):627.
The Logic of Provability.Timothy Williamson - 1996 - Philosophical Quarterly 46 (182):110-116.

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