{
  "id": "1810.10377",
  "version": "v1",
  "published": "2018-10-24T13:02:57.000Z",
  "updated": "2018-10-24T13:02:57.000Z",
  "title": "On Strongly NIP Ordered Fields",
  "authors": [
    "Lothar Sebastian Krapp",
    "Salma Kuhlmann"
  ],
  "comment": "11 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "The following conjecture is due to Shelah$-$Hasson: Any infinite strongly NIP field is either real closed, algebraically closed, or it admits a non-trivial definable henselian valuation, in the language $\\mathcal{L}_{\\mathrm{r}} = \\{+,-,\\cdot,0,1\\}$. Inspired by this, we formulate an analogous conjecture for ordered fields in the language $\\mathcal{L}_{\\mathrm{or}} = \\mathcal{L}_{\\mathrm{r}} \\cup \\{<\\}$. Moreover, we examine strongly NIP almost real closed fields as well as ordered Hahn fields and exhibit connections to ordered fields which are not dense in their real closure and dp-minimal ordered fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-24T13:02:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strongly nip ordered fields",
      "infinite strongly nip field",
      "non-trivial definable henselian valuation",
      "dp-minimal ordered fields",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}