The strength of sharply bounded induction requires MSP

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Abstract

We show that the arithmetical theory T20+Σˆ1b-INDx5, formalized in the language of Buss, i.e. with x/2 but without the MSP function x/2y, does not prove that every nontrivial divisor of a power of 2 is even. It follows that this theory proves neither NP=coNP nor S20.

MSC

03F30

Keywords

Bounded arithmetic
Very weak arithmetic
Sharply bounded formulas
Unconditional independence results

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