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

Pudlak, P (Academy of Sciences, Prague)
Monday 10 April 2006, 10:00-11:00

Seminar Room 1, Newton Institute


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.


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