{
  "id": "2210.01567",
  "version": "v1",
  "published": "2022-10-04T12:45:46.000Z",
  "updated": "2022-10-04T12:45:46.000Z",
  "title": "Extension bases in Henselian valued fields",
  "authors": [
    "Akash Hossain"
  ],
  "comment": "37 pages, no figure, prepublication",
  "categories": [
    "math.LO"
  ],
  "abstract": "We give several sufficient conditions for parameter sets in a Henselian valued field of residue characteristic zero to be an extension base. This enables us in particular to show that forking coincides with dividing in (the $^{eq}$ expansions of) some classical valued fields of residue characteristic zero, like the ultraproducts of the $p$-adic fields, or the field of Laurent series over $\\mathbb{C}$. The strategy is to look for easy sufficient conditions for some unary types to be non-forking, and then use a standard induction argument.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-04T12:45:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "03C52",
      "03C45",
      "12J10",
      "12L12"
    ],
    "keywords": [
      "henselian valued field",
      "extension base",
      "residue characteristic zero",
      "sufficient conditions",
      "standard induction argument"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}