{
  "id": "2102.13141",
  "version": "v1",
  "published": "2021-02-25T19:38:50.000Z",
  "updated": "2021-02-25T19:38:50.000Z",
  "title": "Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History",
  "authors": [
    "Saul A. Kripke"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long 'search' for a purely mathematical incompleteness result in first-order arithmetic. This paper questions the existence of any such search and the status of the Paris-Harrington result as the first mathematical incompleteness result. In fact, I argue that Gentzen gave the first such result, and that it was restated by Goodstein in a number-theoretic form.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-25T19:38:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "first-order peano arithmetic",
      "revisionist view",
      "early history",
      "first mathematical incompleteness result",
      "number-theoretic form"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}