Propositional proof systems, the consistency of first order theories and the complexity of computations

Journal of Symbolic Logic 54 (3):1063-1079 (1989)
We consider the problem about the length of proofs of the sentences $\operatorname{Con}_S(\underline{n})$ saying that there is no proof of contradiction in S whose length is ≤ n. We show the relation of this problem to some problems about propositional proof systems
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DOI 10.2307/2274765
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References found in this work BETA
On the Scheme of Induction for Bounded Arithmetic Formulas.A. J. Wilkie & J. B. Paris - 1987 - Annals of Pure and Applied Logic 35 (3):261-302.

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Citations of this work BETA
Propositional Consistency Proofs.Samuel R. Buss - 1991 - Annals of Pure and Applied Logic 52 (1-2):3-29.
Tautologies From Pseudo-Random Generators.Jan Krajicek - 2001 - Bulletin of Symbolic Logic 7 (2):197-212.
Extension Without Cut.Lutz Straßburger - 2012 - Annals of Pure and Applied Logic 163 (12):1995-2007.
Consistency, Optimality, and Incompleteness.Yijia Chen, Jörg Flum & Moritz Müller - 2013 - Annals of Pure and Applied Logic 164 (12):1224-1235.

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