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On the provability logic of bounded arithmetic
Annals of Pure and Applied Logic 61 (1-2):75-93 (1991)
Abstract
Let PLω be the provability logic of IΔ0 + ω1. We prove some containments of the form L ⊆ PLω < Th(C) where L is the provability logic of PA and Th(C) is a suitable class of Kripke framesAuthor's Profile
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Citations of this work
Substitutions of Σ10-sentences: explorations between intuitionistic propositional logic and intuitionistic arithmetic.Albert Visser - 2002 - Annals of Pure and Applied Logic 114 (1-3):227-271.
Montague’s Paradox, Informal Provability, and Explicit Modal Logic.Walter Dean - 2014 - Notre Dame Journal of Formal Logic 55 (2):157-196.
The interpretability logic of all reasonable arithmetical theories.Joost J. Joosten & Albert Visser - 2000 - Erkenntnis 53 (1-2):3-26.
The Second Incompleteness Theorem and Bounded Interpretations.Albert Visser - 2012 - Studia Logica 100 (1-2):399-418.
Bimodal logics for extensions of arithmetical theories.Lev D. Beklemishev - 1996 - Journal of Symbolic Logic 61 (1):91-124.
References found in this work
On the scheme of induction for bounded arithmetic formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (C):261-302.
Cuts, consistency statements and interpretations.Pavel Pudlák - 1985 - Journal of Symbolic Logic 50 (2):423-441.
Review of Robert M. Solovay's Provability Interpretations of Modal Logic.George Boolos - 1981 - Journal of Symbolic Logic 46 (3):661-662.
Modal analysis of generalized Rosser sentences.Vítězslav Švejdar - 1983 - Journal of Symbolic Logic 48 (4):986-999.
The Decision Problem for Exponential Diophantine Equations.Martin Davis, Hilary Putnam & Julia Robinson - 1970 - Journal of Symbolic Logic 35 (1):151-152.
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