{
  "id": "0905.4412",
  "version": "v1",
  "published": "2009-05-26T11:22:59.000Z",
  "updated": "2009-05-26T11:22:59.000Z",
  "title": "Weak systems of determinacy and arithmetical quasi-inductive definitions",
  "authors": [
    "P. D. Welch"
  ],
  "comment": "submitted; this is a revised version of an unsubmitted July 2003 preprint, now with a minimally improved upper bound",
  "categories": [
    "math.LO"
  ],
  "abstract": "We locate winning strategies for various Sigma^0_3-games in the L-hierarchy in order to prove that Sigma^0_3 Determinacy is intermediate between Pi^1_3-CA_0 (even Pi^1_2-CA_0 (lightface) with Pi^1_3-lightface definable parameters allowed) and Delta^1_3-CA_0 + AQI. (Here \"AQI\" is the statement in second order number theory that every arithmeical quasi-inductive definition on any input stabilizes).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-05-26T11:22:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E45",
      "03F45",
      "03E60",
      "03E15"
    ],
    "keywords": [
      "arithmetical quasi-inductive definitions",
      "weak systems",
      "determinacy",
      "second order number theory",
      "locate winning strategies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0905.4412W"
    }
  }
}