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

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

paper

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

arXiv:cmp-lg/9804005

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 $\neq ⊢ P < N P$ .

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?