{
  "id": "2401.06884",
  "version": "v1",
  "published": "2024-01-12T20:30:14.000Z",
  "updated": "2024-01-12T20:30:14.000Z",
  "title": "Definable henselian valuations in positive residue characteristic",
  "authors": [
    "Margarete Ketelsen",
    "Simone Ramello",
    "Piotr Szewczyk"
  ],
  "comment": "18 pages, 3 figures",
  "categories": [
    "math.LO",
    "math.AC"
  ],
  "abstract": "We study the question of $\\mathcal{L}_{\\mathrm{ring}}$-definability of non-trivial henselian valuation rings. Building on previous work of Jahnke and Koenigsmann, we provide a characterization of henselian fields that admit a non-trivial definable henselian valuation. In particular, we treat cases where the canonical henselian valuation has positive residue characteristic, using techniques from the model theory and algebra of tame fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-12T20:30:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "12L12"
    ],
    "keywords": [
      "positive residue characteristic",
      "non-trivial henselian valuation rings",
      "non-trivial definable henselian valuation",
      "canonical henselian valuation",
      "treat cases"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}