English

How to escape Tennenbaum's theorem

Logic 2022-09-05 v1

Abstract

We construct a theory definitionally equivalent to first-order Peano arithmetic PA and a non-standard computable model of this theory. The same technique allows us to construct a theory definitionally equivalent to Zermelo-Fraenkel set theory ZF that has a computable model.

Cite

@article{arxiv.2209.00967,
  title  = {How to escape Tennenbaum's theorem},
  author = {Fedor Pakhomov},
  journal= {arXiv preprint arXiv:2209.00967},
  year   = {2022}
}

Comments

10 pages

R2 v1 2026-06-28T00:37:47.431Z