English

Two remarks on proof theory of first-order arithmetic

Logic 2021-01-01 v2

Abstract

In this note let us give two remarks on proof-theory of PA. First a derivability relation is introduced to bound witnesses for provable Σ1\Sigma_{1}-formulas in PA. Second Paris-Harrington's proof for their independence result is reformulated to show a `consistency' proof of PA based on a combinatorial principle.

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Cite

@article{arxiv.2003.13207,
  title  = {Two remarks on proof theory of first-order arithmetic},
  author = {Toshiyasu Arai},
  journal= {arXiv preprint arXiv:2003.13207},
  year   = {2021}
}
R2 v1 2026-06-23T14:31:19.401Z