On the provability logic of bounded arithmetic

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Annals of Pure and Applied Logic 61 (1-2):75-93 (1991)
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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 frames

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1993

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10.1016/0168-0072(93)90199-n

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Citations of this work

Montague’s Paradox, Informal Provability, and Explicit Modal Logic.Walter Dean - 2014 - Notre Dame Journal of Formal Logic 55 (2):157-196.
Bimodal logics for extensions of arithmetical theories.Lev D. Beklemishev - 1996 - Journal of Symbolic Logic 61 (1):91-124.

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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.
Modal analysis of generalized Rosser sentences.Vítězslav Švejdar - 1983 - Journal of Symbolic Logic 48 (4):986-999.

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