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.George S. Boolos - 1993 - Cambridge and New York: Cambridge University Press.
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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Citations of this work BETA

Another Look at the Second Incompleteness Theorem.Albert Visser - 2020 - Review of Symbolic Logic 13 (2):269-295.
The Absorption Law: Or: How to Kreisel a Hilbert–Bernays–Löb.Albert Visser - 2020 - Archive for Mathematical Logic 60 (3-4):441-468.
Rosser Provability and Normal Modal Logics.Taishi Kurahashi - 2020 - Studia Logica 108 (3):597-617.

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