On the existence of certain total recursive functions in nontrivial axiom systems, I
<|reference_start|>On the existence of certain total recursive functions in nontrivial axiom systems, I: 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$\not\vdash P<NP$.<|reference_end|>
@article{da costa1998on,
    title={On the existence of certain total recursive functions in nontrivial
  axiom systems, I},
    author={N. C. A. da Costa (University of Sao Paulo) and F. A. Doria (Federal
  University at Rio de Janeiro)},
    journal={arXiv preprint arXiv:cmp-lg/9804005},
    year={1998},
    archivePrefix={arXiv},
    eprint={cmp-lg/9804005},
    primaryClass={cmp-lg cs.CL}
}