# LAA

## Seminar

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

Seminar Room 1, Newton Institute

#### 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.