{
  "id": "1210.7615",
  "version": "v4",
  "published": "2012-10-29T10:52:35.000Z",
  "updated": "2014-07-31T08:35:38.000Z",
  "title": "Definable henselian valuations",
  "authors": [
    "Franziska Jahnke",
    "Jochen Koenigsmann"
  ],
  "comment": "14 pages, revised version",
  "categories": [
    "math.LO"
  ],
  "abstract": "In this note we investigate the question whether a henselian valued field carries a non-trivial 0-definable henselian valuation (in the language of rings). It follows from the work of Prestel and Ziegler that there are henselian valued fields which do not admit a 0-definable non-trivial henselian valuation. We give conditions on the residue field which ensure the existence of a parameter-free definiton. In particular, we show that a henselian valued field admits a non-trivial 0-definable valuation when the residue field is separably closed or sufficiently non-henselian, or when the absolute Galois group of the (residue) field is non-universal.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2014-07-31T08:35:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C40",
      "12E30",
      "12J10",
      "03C60",
      "12L12"
    ],
    "keywords": [
      "definable henselian valuations",
      "residue field",
      "henselian valued field carries",
      "non-trivial henselian valuation",
      "henselian valued field admits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.7615J"
    }
  }
}