What are the ∀∑1 b-consequences of T 2 1 and T 2 2?

Annals of Pure and Applied Logic 75 (1):79-88 (1995)
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Abstract

We formulate schemes and of the “typical” ∀∑ 1 b -sentences that are provable in T 2 1, respectively T 2 2. As an application, we reprove a recent result of Buss and Krajíček which describes witnesses for the ∀∑ 1 b -sentences provable in T 2 1 in terms of solutions to PLS-problems.

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10.1016/0168-0072(94)00059-c

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Bounded arithmetic and the polynomial hierarchy.Jan Krajíček, Pavel Pudlák & Gaisi Takeuti - 1991 - Annals of Pure and Applied Logic 52 (1-2):143-153.

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