The strength of sharply bounded induction requires M S P

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Annals of Pure and Applied Logic 161 (4):504-510 (2010)
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Abstract

We show that the arithmetical theory -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

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10.1016/j.apal.2009.03.002

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Citations of this work

Open induction in a bounded arithmetic for TC0.Emil Jeřábek - 2015 - Archive for Mathematical Logic 54 (3-4):359-394.
On the finite axiomatizability of.Chris Pollett - 2018 - Mathematical Logic Quarterly 64 (1-2):6-24.

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References found in this work

Multifunction algebras and the provability of PH↓.Chris Pollett - 2000 - Annals of Pure and Applied Logic 104 (1-3):279-303.
The strength of sharply bounded induction.Emil Jeřábek - 2006 - Mathematical Logic Quarterly 52 (6):613-624.

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