{
  "id": "math/0406505",
  "version": "v1",
  "published": "2004-06-24T19:09:54.000Z",
  "updated": "2004-06-24T19:09:54.000Z",
  "title": "The Isomorphism Problem for Computable Abelian p-Groups of Bounded Length",
  "authors": [
    "Wesley Calvert"
  ],
  "comment": "15 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Theories of classification distinguish classes with some good structure theorem from those for which none is possible. Some classes (dense linear orders, for instance) are non-classifiable in general, but are classifiable when we consider only countable members. This paper explores such a notion for classes of computable structures by working out a sequence of examples. We follow recent work by Goncharov and Knight in using the degree of the isomorphism problem for a class to distinguish classifiable classes from non-classifiable. In this paper, we calculate the degree of the isomorphism problem for Abelian $p$-groups of bounded Ulm length. The result is a sequence of classes whose isomorphism problems are cofinal in the hyperarithmetical hierarchy. In the process, new back-and-forth relations on such groups are calculated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-24T19:09:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C57",
      "20K10"
    ],
    "keywords": [
      "isomorphism problem",
      "computable abelian p-groups",
      "bounded length",
      "dense linear orders",
      "structure theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6505C"
    }
  }
}