{
  "id": "math/0612234",
  "version": "v1",
  "published": "2006-12-09T15:12:59.000Z",
  "updated": "2006-12-09T15:12:59.000Z",
  "title": "Recursive definitions on surreal numbers",
  "authors": [
    "Antongiulio Fornasiero"
  ],
  "categories": [
    "math.LO",
    "math.RA"
  ],
  "abstract": "Let No be Conway's class of surreal numbers. I will make explicit the notion of a function f on No recursively defined over some family of functions. Under some \"tameness\" and uniformity condition, f must satisfy some interesting properties; in particular, the supremum of the class of element greater or equal to a fixed d in No is actually an element of No. For similar reasons, the concatenation function x:y cannot be defined recursively in a uniform way over polynomial functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-12-09T15:12:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "03C65",
      "03H05",
      "12J15",
      "20F60"
    ],
    "keywords": [
      "surreal numbers",
      "recursive definitions",
      "concatenation function",
      "similar reasons",
      "polynomial functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12234F"
    }
  }
}