{
  "id": "0810.0734",
  "version": "v2",
  "published": "2008-10-03T23:24:04.000Z",
  "updated": "2019-08-18T14:54:25.000Z",
  "title": "Unstable classes of metric structures",
  "authors": [
    "Saharon Shelah",
    "Alexander Usvyatsov"
  ],
  "categories": [
    "math.LO",
    "math.FA"
  ],
  "abstract": "We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several versions of stability. This is the first step in the direction of the investigation of weak categoricity and weak stability of metric classes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-10-03T23:24:04.000Z",
      "abstract": "We prove a strong nonstructure theorem for a class of metric structures with an unstable formula. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several versions of stability. This is the first step in the direction of the investigation of weak categoricity of metric classes.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2019-08-18T14:54:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric structures",
      "unstable classes",
      "weak categoricity",
      "strong nonstructure theorem",
      "first step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0734S"
    }
  }
}