On bimodal logics of provability
type: Item
instance of: scholarly article
title: On bimodal logics of provability
zbMATH Open document ID: 0814.03010
DOI: 10.1016/0168-0072(94)90071-X
author: Lev D. Beklemishev
published in: Annals of Pure and Applied Logic
publication date: 1994-10-13T00:00:00Z
review text: The author investigates the bimodal logics sound and complete under the interpretation of modal operators as the provability predicates in certain natural pairs of arithmetical theories \(({\mathcal T},{\mathcal U})\). He studies those pairs of theories \(({\mathcal T},{\mathcal U})\) for which \({\mathcal U}\) is axiomatized over \({\mathcal T}\) by \(\Pi_ 1\)-sentences only, and for each \(n\geq 1\), \({\mathcal U}\) proves the \(n\)-times iterated consistency of \({\mathcal T}\). A complete axiomatization, along with the appropriate Kripke semantics and decision procedures, is found for the two principal cases: finitely axiomatizable extensions of this sort and reflexive extensions of this sort.
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 633658
zbMATH Keywords: Kalmar elementary arithmetic
zbMATH Keywords: provability logic
zbMATH Keywords: bimodal logics
zbMATH Keywords: complete axiomatization
zbMATH Keywords: Kripke semantics
zbMATH Keywords: decision procedures
reviewed by: Lei Qian
MaRDI profile type: Publication
cites work: Q3731573
cites work: Q3912553
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full work available at URL: 0168-0072(94)90071-x
OpenAlex ID: W1987969414
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description: scientific article; zbMATH DE number 633658