{
  "id": "2008.09889",
  "version": "v1",
  "published": "2020-08-22T18:00:00.000Z",
  "updated": "2020-08-22T18:00:00.000Z",
  "title": "Distality in Valued Fields and Related Structures",
  "authors": [
    "Matthias Aschenbrenner",
    "Artem Chernikov",
    "Allen Gehret",
    "Martin Ziegler"
  ],
  "comment": "58 pp",
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an AKE-style characterization for henselian valued fields, and demonstrate that certain expansions of fields, e.g., the differential field of logarithmic-exponential transseries, are distal. As a new tool for analyzing valued fields we employ a relative quantifier elimination for pure short exact sequences of abelian groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-22T18:00:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C60",
      "12L12",
      "12J25"
    ],
    "keywords": [
      "related structures",
      "pure short exact sequences",
      "ake-style characterization",
      "distal expansions",
      "differential field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 58,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}