{
  "id": "2003.13207",
  "version": "v1",
  "published": "2020-03-30T03:56:02.000Z",
  "updated": "2020-03-30T03:56:02.000Z",
  "title": "Two remarks on proof theory of first-order arithmetic",
  "authors": [
    "Toshiyasu Arai"
  ],
  "categories": [
    "math.LO"
  ],
  "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 $\\Sigma_{1}$-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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-30T03:56:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F30"
    ],
    "keywords": [
      "proof theory",
      "first-order arithmetic",
      "second paris-harringtons proof",
      "bound witnesses",
      "combinatorial principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}