An Isaac Newton Institute Workshop

New Directions in Proof Complexity

On \forall\Sigma_1^b sentences provable in bounded arithmetic

Author: P Pudlak (Academy of Sciences, Prague)

Abstract

We shall give a characterization of \forall\Sigma_1^b sentences provable in theories S_2^i. We shall consider also certain unrestricted versions of the principles that characterize these sentences and prove that they require iterated exponential time. This gives partial evidence that the hierarchy of \forall\Sigma_1^b sentences provable in S_2^i is strictly increasing.