## Journal of Symbolic Logic

### Propositional Proof Systems, the Consistency of First Order Theories and the Complexity of Computations

#### Abstract

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 $\leq n$. We show the relation of this problem to some problems about propositional proof systems.

#### Article information

Source
J. Symbolic Logic, Volume 54, Issue 3 (1989), 1063-1079.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183743040

Mathematical Reviews number (MathSciNet)
MR1011192

Zentralblatt MATH identifier
0696.03029

JSTOR