{
  "id": "2311.00411",
  "version": "v1",
  "published": "2023-11-01T10:04:47.000Z",
  "updated": "2023-11-01T10:04:47.000Z",
  "title": "Relative model completeness of henselian valued fields with finite ramification and various value groups",
  "authors": [
    "Anna De Mase"
  ],
  "comment": "22 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate the model completeness of a mixed characteristic henselian valued field with finite ramification relative to the residue field and value group. We address the case in which the valued field has a value group with finite spines, and the case in which the value group is elementarily equivalent to the infinite lexicographic sum of $\\mathbb{Z}$ with a minimal positive element. In both cases, we find a one-sorted language in which the theory of the valued field is model complete, if the theory of the residue field is model complete in the language of rings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-01T10:04:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "value group",
      "relative model completeness",
      "finite ramification",
      "residue field",
      "infinite lexicographic sum"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}