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Provability logics for natural Turing progressions of arithmetical theories
Studia Logica 50 (1):107-128 (1991)
Abstract
Provability logics with many modal operators for progressions of theories obtained by iterating their consistency statements are introduced. The corresponding arithmetical completeness theorem is proved.Author's Profile
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Citations of this work
The omega-rule interpretation of transfinite provability logic.David Fernández-Duque & Joost J. Joosten - 2018 - Annals of Pure and Applied Logic 169 (4):333-371.
On bimodal logics of provability.Lev D. Beklemishev - 1994 - Annals of Pure and Applied Logic 68 (2):115-159.
Bimodal logics for extensions of arithmetical theories.Lev D. Beklemishev - 1996 - Journal of Symbolic Logic 61 (1):91-124.
On the inevitability of the consistency operator.Antonio Montalbán & James Walsh - 2019 - Journal of Symbolic Logic 84 (1):205-225.
References found in this work
Transfinite recursive progressions of axiomatic theories.Solomon Feferman - 1962 - Journal of Symbolic Logic 27 (3):259-316.
Provability in finite subtheories of pa and relative interpretability: A modal investigation.Franco Montagna - 1987 - Journal of Symbolic Logic 52 (2):494-511.
Quantified modal logic and self-reference.C. Smoryński - 1987 - Notre Dame Journal of Formal Logic 28 (3):356-370.
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