### Propositional Proof Systems and Fast Consistency Provers

Joost J. Joosten
Source: Notre Dame J. Formal Logic Volume 48, Number 3 (2007), 381-398.

#### Abstract

A fast consistency prover is a consistent polytime axiomatized theory that has short proofs of the finite consistency statements of any other polytime axiomatized theory. Krajíček and Pudlák have proved that the existence of an optimal propositional proof system is equivalent to the existence of a fast consistency prover. It is an easy observation that NP = coNP implies the existence of a fast consistency prover. The reverse implication is an open question. In this paper we define the notion of an unlikely fast consistency prover and prove that its existence is equivalent to NP = coNP. Next it is proved that fast consistency provers do not exist if one considers RE axiomatized theories rather than theories with an axiom set that is recognizable in polynomial time.

First Page:
Primary Subjects: 03B70
Secondary Subjects: 68Q15
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1187031410
Digital Object Identifier: doi:10.1305/ndjfl/1187031410
Mathematical Reviews number (MathSciNet): MR2336354
Zentralblatt MATH identifier: 1133.03036

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