On the existence of certain total recursive functions in nontrivial axiom systems, I

N. C. A. da Costa; F. A. Doria

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arXiv · cmp-lg/9804005

On the existence of certain total recursive functions in nontrivial axiom systems, I

N. C. A. da Costa·F. A. Doria

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Abstract

We investigate the existence of a class of ZFC-provably total recursive unary functions, given certain constraints, and apply some of those results to show that, for $Σ_1$-sound set theory, ZFC$\not\vdash P<NP$.

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N. C. A. da Costa, F. A. Doria. 1998-04-30. On the existence of certain total recursive functions in nontrivial axiom systems, I. https://arxiv.org/abs/cmp-lg/9804005

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