{
  "id": "1602.01156",
  "version": "v1",
  "published": "2016-02-02T23:52:28.000Z",
  "updated": "2016-02-02T23:52:28.000Z",
  "title": "Hanf Number for Scott Sentences of Computable Structures",
  "authors": [
    "Sergey Goncharov",
    "Julia Knight",
    "Ioannis Souldatos"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The Hanf number for a set $S$ of sentences in $L_{\\omega_1,\\omega}$ (or some other logic) is the least infinite cardinal $\\kappa$ such that for all $\\varphi\\in S$, if $\\varphi$ has models in all infinite cardinalities less than $\\kappa$, then it has models of all infinite cardinalities. S-D. Friedman asked what is the Hanf number for Scott sentences of computable structures. We show that the value is $\\beth_{\\omega_1^{CK}}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-02T23:52:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hanf number",
      "scott sentences",
      "computable structures",
      "infinite cardinalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201156G"
    }
  }
}