{
  "id": "2001.09243",
  "version": "v1",
  "published": "2020-01-25T01:10:31.000Z",
  "updated": "2020-01-25T01:10:31.000Z",
  "title": "A Barwise-Schlipf Theorem for Set Theory",
  "authors": [
    "Ali Enayat"
  ],
  "comment": "14 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We characterize nonstandard models of ZF (Zermelo-Fraenkel) set theory (of arbitrary cardinality) that can be expanded to Goedel-Bernays class theory plus $\\Delta^1_1$-Comprehension. We also characterize countable nonstandard models of ZFC (ZF with the axiom of choice) that can be expanded to Goedel-Bernays class theory plus $\\Sigma^1_1$-Choice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-25T01:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C62",
      "03E30"
    ],
    "keywords": [
      "set theory",
      "barwise-schlipf theorem",
      "goedel-bernays class theory plus",
      "arbitrary cardinality",
      "characterize nonstandard models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}