{
  "id": "1906.00645",
  "version": "v1",
  "published": "2019-06-03T09:04:56.000Z",
  "updated": "2019-06-03T09:04:56.000Z",
  "title": "How strong are single fixed points of normal functions?",
  "authors": [
    "Anton Freund"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In a recent paper by M. Rathjen and the present author it has been shown that the statement ``every normal function has a derivative'' is equivalent to $\\Pi^1_1$-bar induction. The equivalence was proved over $\\mathbf{ACA_0}$, for a suitable representation of normal functions in terms of dilators. In the present paper we show that the statement ``every normal function has at least one fixed point'' is equivalent to $\\Pi^1_1$-induction along the natural numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-03T09:04:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F15",
      "03F35",
      "03D60",
      "03E10"
    ],
    "keywords": [
      "normal function",
      "single fixed points",
      "natural numbers",
      "equivalent",
      "bar induction"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}