{
  "id": "1503.00315",
  "version": "v1",
  "published": "2015-03-01T17:33:51.000Z",
  "updated": "2015-03-01T17:33:51.000Z",
  "title": "Surreal numbers, derivations and transseries",
  "authors": [
    "Alessandro Berarducci",
    "Vincenzo Mantova"
  ],
  "comment": "46 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Several authors have conjectured that Conway's field of surreal numbers, equipped with the exponential function of Kruskal and Gonshor, can be described as a field of transseries and admits a compatible differential structure of Hardy-type. In this paper we give a complete positive solution to both problems. We also show that with this new differential structure, the surreal numbers are Liouville closed, namely the derivation is surjective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-01T17:33:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "16W60",
      "04A10",
      "26A12",
      "13N15"
    ],
    "keywords": [
      "surreal numbers",
      "transseries",
      "derivation",
      "exponential function",
      "compatible differential structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150300315B"
    }
  }
}