The unprovability of small inconsistency

Archive for Mathematical Logic 32 (4):275-298 (1993)
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Abstract

We show that a consistent, finitely axiomatized, sequential theory cannot prove its own inconsistency on every definable cut. A corollary is that there are at least three degrees of global interpretability of theories equivalent modulo local interpretability to a consistent, finitely axiomatized, sequential theory U

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10.1007/bf01387407

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Citations of this work

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A proof-theoretic analysis of collection.Lev D. Beklemishev - 1998 - Archive for Mathematical Logic 37 (5-6):275-296.
Faith & falsity.Albert Visser - 2004 - Annals of Pure and Applied Logic 131 (1-3):103-131.
Rules and Arithmetics.Albert Visser - 1999 - Notre Dame Journal of Formal Logic 40 (1):116-140.
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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.
Existence and feasibility in arithmetic.Rohit Parikh - 1971 - Journal of Symbolic Logic 36 (3):494-508.
Self-Reference and Modal Logic.George Boolos & C. Smorynski - 1988 - Journal of Symbolic Logic 53 (1):306.
Cuts, consistency statements and interpretations.Pavel Pudlák - 1985 - Journal of Symbolic Logic 50 (2):423-441.
Self-Reference and Modal Logic.[author unknown] - 1987 - Studia Logica 46 (4):395-398.

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