{
  "id": "2109.06258",
  "version": "v1",
  "published": "2021-09-13T18:52:57.000Z",
  "updated": "2021-09-13T18:52:57.000Z",
  "title": "Unprovability in Mathematics: A First Course on Ordinal Analysis",
  "authors": [
    "Anton Freund"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "These are the lecture notes of an introductory course on ordinal analysis. Our selection of topics is guided by the aim to give a complete and direct proof of a mathematical independence result: Kruskal's theorem for binary trees is unprovable in conservative extensions of Peano arithmetic (note that much stronger results of this type are due to Harvey Friedman). Concerning prerequisites, we assume a solid introduction to mathematical logic but no specialized knowledge of proof theory. The material in these notes is intended for 14 lectures and 7 exercise sessions of 90 minutes each.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-13T18:52:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03-01",
      "03B30",
      "03F05",
      "03F15",
      "03F35",
      "03F40"
    ],
    "keywords": [
      "ordinal analysis",
      "first course",
      "unprovability",
      "mathematics",
      "introductory course"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}