{
  "id": "1501.04522",
  "version": "v1",
  "published": "2015-01-19T15:27:54.000Z",
  "updated": "2015-01-19T15:27:54.000Z",
  "title": "The existential theory of equicharacteristic henselian valued fields",
  "authors": [
    "Will Anscombe",
    "Arno Fehm"
  ],
  "categories": [
    "math.LO",
    "math.AC"
  ],
  "abstract": "We study the existential (and parts of the universal-existential) theory of equicharacteristic henselian valued fields. We prove, among other things, an existential Ax-Kochen-Ershov principle, which roughly says that the existential theory of an equicharacteristic henselian valued field (of arbitrary characteristic) is determined by the existential theory of the residue field; in particular, it is independent of the value group. As an immediate corollary, we get an unconditional proof of the decidability of the existential theory of $\\mathbb{F}_{q}((t))$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-19T15:27:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "12L12",
      "12J10",
      "11U05",
      "12L05"
    ],
    "keywords": [
      "equicharacteristic henselian valued field",
      "existential theory",
      "existential ax-kochen-ershov principle",
      "arbitrary characteristic",
      "residue field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150104522A"
    }
  }
}