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

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

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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DOI 10.1007/s11225-017-9735-y
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References found in this work BETA

The Logic of Provability.Philip Scowcroft & George Boolos - 1995 - Philosophical Review 104 (4):627.
The Logic of Provability.George Boolos - 1993 - Philosophical Quarterly 46 (182):110-116.
Four Valued Semantics and the Liar.Albert Visser - 1984 - Journal of Philosophical Logic 13 (2):181 - 212.
A Smart Child of Peano's.V. Yu Shavrukov - 1994 - Notre Dame Journal of Formal Logic 35 (2):161-185.

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