{
  "id": "2305.01635",
  "version": "v1",
  "published": "2023-05-02T17:47:51.000Z",
  "updated": "2023-05-02T17:47:51.000Z",
  "title": "A characterization of saturated models of a finite extension of the $p$-adics through a Hahn-like construction",
  "authors": [
    "Anna De Mase"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We give a characterization of $\\omega$-pseudo complete valued fields elementarily equivalent to a finite extension $L$ of the $p$-adics and with a fixed value group $G$ of cardinality $\\aleph_{1}$ in terms of a Hahn-like construction over $L$, generalizing a result obtained by Ax J. and Kochen S. in '65 for formally $p$-adic fields. We extend this construction to a more general contest of mixed characteristic valued fields with finite ramification.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-02T17:47:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite extension",
      "hahn-like construction",
      "saturated models",
      "characterization",
      "pseudo complete valued fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}