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

Published online by Cambridge University Press:  12 March 2014

Jan Krajíček  and
Pavel Pudlák
Jan Krajíček
Affiliation:
Mathematical Institute, Czechoslovak Academy of Sciences, 115 67 Prague 1, Czechoslovakia
Pavel Pudlák
Affiliation:
Mathematical Institute, Czechoslovak Academy of Sciences, 115 67 Prague 1, Czechoslovakia
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Abstract

We consider the problem about the length of proofs of the sentences 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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 54 , Issue 3 , September 1989 , pp. 1063 - 1079
Copyright
Copyright © Association for Symbolic Logic 1989

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