{
  "id": "2209.06898",
  "version": "v1",
  "published": "2022-09-14T19:52:24.000Z",
  "updated": "2022-09-14T19:52:24.000Z",
  "title": "Borel complexity of modules",
  "authors": [
    "Michael C. Laskowski",
    "Danielle S. Ulrich"
  ],
  "categories": [
    "math.LO",
    "math.AC"
  ],
  "abstract": "We prove that for a countable, commutative ring $R$, the class of countable $R$-modules either has only countably many isomorphism types, or else it is Borel complete. The machinery gives a succinct proof of the Borel completeness of TFAB, the class of torsion-free abelian groups. We also prove that for any countable ring $R$, both the class of left $R$-modules endowed with an endomorphism and the class of left $R$-modules with four named submodules are Borel complete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-14T19:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "13C05"
    ],
    "keywords": [
      "borel complexity",
      "torsion-free abelian groups",
      "isomorphism types",
      "borel completeness",
      "succinct proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}