{
  "id": "1211.5441",
  "version": "v2",
  "published": "2012-11-23T09:02:11.000Z",
  "updated": "2012-11-27T12:44:22.000Z",
  "title": "Separating Models by Formulas and the Number of Countable Models",
  "authors": [
    "Mohammad Assem"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We indicate a way of distinguishing between structures, for which, two structures are said to be separable.Being separable implies being non-isomorphic. We show that for any first order theory $T$ in a countable language, if it has an uncountable set of countable models that are pairwise separable, then actually it has such a set of size $2^{\\aleph_0}$. Our result follows trivially assuming the Continuum Hypothesis ($CH$). We work here in $ZFC$ (only without $CH$).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-27T12:44:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "countable models",
      "separating models",
      "first order theory",
      "structures",
      "continuum hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.5441A"
    }
  }
}