{
  "id": "1512.02267",
  "version": "v1",
  "published": "2015-12-07T22:27:29.000Z",
  "updated": "2015-12-07T22:27:29.000Z",
  "title": "The surreal numbers as a universal H-field",
  "authors": [
    "Matthias Aschenbrenner",
    "Lou van den Dries",
    "Joris van der Hoeven"
  ],
  "comment": "17 pp",
  "categories": [
    "math.LO",
    "math.CA",
    "math.RA"
  ],
  "abstract": "We show that the natural embedding of the differential field of transseries into Conway's field of surreal numbers with the Berarducci-Mantova derivation is an elementary embedding. We also prove that any Hardy field embeds into the field of surreals with the Berarducci-Mantova derivation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-07T22:27:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "surreal numbers",
      "universal h-field",
      "berarducci-mantova derivation",
      "hardy field embeds",
      "differential field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151202267A"
    }
  }
}