{
  "id": "1801.09411",
  "version": "v1",
  "published": "2018-01-29T09:18:29.000Z",
  "updated": "2018-01-29T09:18:29.000Z",
  "title": "Hyperbolicity and Cubulability Are Preserved Under Elementary Equivalence",
  "authors": [
    "Simon André"
  ],
  "categories": [
    "math.GR",
    "math.LO"
  ],
  "abstract": "The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated group G has the same first-order theory as a group possessing one of the previous property, then G enjoys this property as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-29T09:18:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elementary equivalence",
      "hyperbolicity",
      "finitely generated group",
      "cubulability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}