{
  "id": "2010.14770",
  "version": "v1",
  "published": "2020-10-27T11:11:43.000Z",
  "updated": "2020-10-27T11:11:43.000Z",
  "title": "Strongly NIP almost real closed fields",
  "authors": [
    "Lothar Sebastian Krapp",
    "Salma Kuhlmann",
    "Gabriel Lehéricy"
  ],
  "comment": "A previous version of this preprint was part of arXiv:1810.10377. arXiv admin note: text overlap with arXiv:2010.11832",
  "categories": [
    "math.LO"
  ],
  "abstract": "The following conjecture is due to Shelah-Hasson: Any infinite strongly NIP field is either real closed, algebraically closed, or admits a non-trivial definable henselian valuation, in the language of rings. We specialise this conjecture to ordered fields in the language of ordered rings, which leads towards a systematic study of the class of strongly NIP almost real closed fields. As a result, we obtain a complete characterisation of this class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-27T11:11:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C64",
      "03C60",
      "12J10",
      "12L12"
    ],
    "keywords": [
      "real closed fields",
      "infinite strongly nip field",
      "non-trivial definable henselian valuation",
      "conjecture",
      "complete characterisation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}