{
  "id": "0805.1887",
  "version": "v1",
  "published": "2008-05-13T17:15:36.000Z",
  "updated": "2008-05-13T17:15:36.000Z",
  "title": "Effective categoricity of equivalence Structures",
  "authors": [
    "W. Calvert",
    "D. Cenzer",
    "V. S. Harizanov",
    "A. Morozov"
  ],
  "comment": "Improved form published",
  "journal": "Annals of Pure and Applied Logic 141 (2006) 61--78",
  "categories": [
    "math.LO"
  ],
  "abstract": "An equivalence structure is a set with a single binary relation, satisfying sentences stating that the relation is an equivalence relation. A computable structure A is said to be $\\Delta^0_\\alpha$ categorical if for any computable structure B isomorphic to A there is a $\\Delta^0_\\alpha$ function witnessing that the two are isomorphic. The present paper gives an exact characterization of $\\Delta^0_\\alpha$ equivalence structures where $\\alpha = 1$ or $\\alpha \\geq 3$. Extensive results for $\\alpha = 2$ are also given, and open cases are exhaustively described.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-13T17:15:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03D45",
      "03C57"
    ],
    "keywords": [
      "equivalence structure",
      "effective categoricity",
      "single binary relation",
      "computable structure",
      "equivalence relation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.1887C"
    }
  }
}