{
  "id": "math/0602541",
  "version": "v1",
  "published": "2006-02-24T03:09:48.000Z",
  "updated": "2006-02-24T03:09:48.000Z",
  "title": "First-order definitions in function fields over anti-Mordellic fields",
  "authors": [
    "Bjorn Poonen",
    "Florian Pop"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT",
    "math.LO"
  ],
  "abstract": "A field k is called anti-Mordellic if every smooth curve over k with a k-point has infinitely many k-points. We prove that for a function field over an anti-Mordellic field, the subfield of constants is defined by a certain universal first order formula. Under additional hypotheses regarding 2-cohomological dimension we prove that algebraic dependence of an n-tuple of elements in such a function field can be described by a first order formula, for each n. We also give a result that lets one distinguish various classes of fields using first order sentences.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-02-24T03:09:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11U09",
      "14G25"
    ],
    "keywords": [
      "function field",
      "anti-mordellic field",
      "first-order definitions",
      "universal first order formula",
      "first order sentences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......2541P"
    }
  }
}