{
  "id": "0910.2682",
  "version": "v1",
  "published": "2009-10-14T18:08:01.000Z",
  "updated": "2009-10-14T18:08:01.000Z",
  "title": "Relative decidability and definability in henselian valued fields",
  "authors": [
    "Joseph Flenner"
  ],
  "comment": "20 pages",
  "journal": "J. Symbolic Logic 76 (2011), no. 4, 1240--1260",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let K be a henselian valued field of characteristic 0. Then K admits a definable partition on each piece of which the leading term of a polynomial in one variable can be computed as a definable function of the leading term of a linear map. Two applications are given: first, a constructive quantifier elimination relative to the leading terms, suggesting a relative decision procedure; second, a presentation of every definable subset of K as the pullback of a definable set in the leading terms subjected to a linear translation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-14T18:08:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "12J10",
      "12L05"
    ],
    "keywords": [
      "henselian valued field",
      "leading term",
      "relative decidability",
      "definability",
      "linear translation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.2682F"
    }
  }
}