{
  "id": "1311.1865",
  "version": "v1",
  "published": "2013-11-08T02:01:58.000Z",
  "updated": "2013-11-08T02:01:58.000Z",
  "title": "The decomposability problem for torsion-free abelian groups is analytic complete",
  "authors": [
    "Kyle Riggs"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We discuss the decomposability of torsion-free abelian groups. We show that among computable groups of finite rank this property is $\\Sigma^0_3$-complete. However, when we consider groups of infinite rank, it becomes $\\Sigma^1_1$-complete, so it cannot be characterized by a first-order formula in the language of arithmetic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-08T02:01:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03D45",
      "03C57"
    ],
    "keywords": [
      "torsion-free abelian groups",
      "analytic complete",
      "decomposability problem",
      "infinite rank",
      "first-order formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.1865R"
    }
  }
}