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

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

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 \.

Categories

Keywords

Reprint years

DOI

10.1007/s11225-017-9735-y

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,139

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Arithmetical interpretations and Kripke frames of predicate modal logic of provability.Taishi Kurahashi - 2013 - Review of Symbolic Logic 6 (1):1-18.
Interpretability over peano arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Interpretability over peano arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Interpretability over peano arithmetic.Claes Strannegård - 1999 - Journal of Symbolic Logic 64 (4):1407-1425.
Generic Generalized Rosser Fixed Points.Dick H. J. de Jongh & Franco Montagna - 1987 - Studia Logica 46 (2):193-203.
Generic generalized Rosser fixed points.Dick H. J. Jongh & Franco Montagna - 1987 - Studia Logica 46 (2):193 - 203.
Provability logic in the Gentzen formulation of arithmetic.Paolo Gentilini & P. Gentilini - 1992 - Mathematical Logic Quarterly 38 (1):535-550.
Syntactical results on the arithmetical completeness of modal logic.Paolo Gentilini - 1993 - Studia Logica 52 (4):549 - 564.
Proof-theoretic modal PA-Completeness III: The syntactic proof.Paolo Gentilini - 1999 - Studia Logica 63 (3):301-310.
On the proof of Solovay's theorem.Dick Jongh, Marc Jumelet & Franco Montagna - 1991 - Studia Logica 50 (1):51 - 69.
On the proof of Solovay's theorem.Dick de Jongh, Marc Jumelet & Franco Montagna - 1991 - Studia Logica 50 (1):51-69.
Finite Kripke models and predicate logics of provability.Sergei Artemov & Giorgie Dzhaparidze - 1990 - Journal of Symbolic Logic 55 (3):1090-1098.
A Sahlqvist theorem for relevant modal logics.Takahiro Seki - 2003 - Studia Logica 73 (3):383-411.
A Sahlqvist Theorem for Relevant Modal Logics.Takahiro Seki - 2003 - Studia Logica 73 (3):383-411.
On the proof-theory of a first-order extension of GL.Yehuda Schwartz & George Tourlakis - 2014 - Logic and Logical Philosophy 23 (3).

Analytics

Added to PP
2017-06-09

Downloads
20 (#703,484)

6 months
5 (#441,012)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Current Research on Gödel’s Incompleteness Theorems.Yong Cheng - 2021 - Bulletin of Symbolic Logic 27 (2):113-167.
Another look at the second incompleteness theorem.Albert Visser - 2020 - Review of Symbolic Logic 13 (2):269-295.
Rosser Provability and Normal Modal Logics.Taishi Kurahashi - 2020 - Studia Logica 108 (3):597-617.

View all 7 citations / Add more citations

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.

View all 10 references / Add more references