{
  "id": "1101.5660",
  "version": "v5",
  "published": "2011-01-29T03:23:41.000Z",
  "updated": "2013-03-11T03:20:35.000Z",
  "title": "Lifting up the proof theory to the countables : Zermelo-Fraenkel set theory",
  "authors": [
    "Toshiyasu Arai"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We describe the countable ordinals in terms of iterations of Mostowski collapsings. This gives a proof-theoretic bound of definable countable ordinals in the Zermelo-Fraenkel's set theory ZF.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2013-03-11T03:20:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F03"
    ],
    "keywords": [
      "zermelo-fraenkel set theory",
      "proof theory",
      "zermelo-fraenkels set theory zf",
      "proof-theoretic bound",
      "mostowski collapsings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1101.5660A"
    }
  }
}