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

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

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

cmp-lg 2007-05-23 v1 Computation and Language

Authors: N. C. A. da Costa , F. A. Doria

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 $\Sigma_1$ -sound set theory, ZFC $\not\vdash P<NP$ .

Keywords

total recursive functions ZFC axiom systems P versus NP Sigma_1-sound set theory provability

Cite

@article{arxiv.cmp-lg/9804005,
  title  = {On the existence of certain total recursive functions in nontrivial axiom systems, I},
  author = {N. C. A. da Costa and F. A. Doria},
  journal= {arXiv preprint arXiv:cmp-lg/9804005},
  year   = {2007}
}

Comments

LaTeX, 16 pages, no figures. This paper was submitted to a major journal in the field and rejected. The referee somehow misundesrtood Corollary 3.8 and wrongly concluded that the proof had either a gap or an error. Can you find whether that error exists?

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

Abstract

Keywords

Cite

Comments

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