{
  "id": "1406.5980",
  "version": "v4",
  "published": "2014-06-23T17:02:24.000Z",
  "updated": "2014-08-28T14:09:41.000Z",
  "title": "Tameness and frames revisited",
  "authors": [
    "Will Boney",
    "Sebastien Vasey"
  ],
  "comment": "31 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We combine tameness for types of singleton with the existence of a good frame to obtain some amount of tameness for types of longer sequences. We use this to show how to use tameness to extend a good frame in one cardinality to a good frame in all cardinalities, improving a theorem of Boney. Along the way, we prove many general results on the independent sequences induced by the good frame. In particular, we show that tameness and a good frame imply Shelah's notion of dimension is well-behaved, complementing previous work of Jarden and Sitton.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-01T12:58:25.000Z",
      "abstract": "We combine tameness for $1$-types with the existence of a good frame to obtain some amount of tameness for $n$-types, where $n$ is a natural number. We use this to show how to use tameness to extend a good frame in one cardinality to a good frame in all cardinalities, improving a theorem of Boney [Bon].",
      "comment": "Draft. 30 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-08-28T14:09:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C48",
      "03C47",
      "03C52",
      "03C55"
    ],
    "keywords": [
      "cardinality",
      "natural number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.5980B"
    }
  }
}