{
  "id": "1510.00964",
  "version": "v1",
  "published": "2015-10-04T18:20:40.000Z",
  "updated": "2015-10-04T18:20:40.000Z",
  "title": "Metric dimensions and tameness in expansions of the real field",
  "authors": [
    "Philipp Hieronymi",
    "Chris Miller"
  ],
  "categories": [
    "math.LO",
    "math.MG"
  ],
  "abstract": "For first-order expansions of the field of real numbers, nondefinability of the set of natural numbers is equivalent to equality of topological and Assouad dimension on images of closed definable sets under definable continuous maps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-04T18:20:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "03E15",
      "28A05",
      "28A75",
      "54F45",
      "54H05"
    ],
    "keywords": [
      "real field",
      "metric dimensions",
      "first-order expansions",
      "natural numbers",
      "assouad dimension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151000964H"
    }
  }
}