{
  "id": "1712.00057",
  "version": "v1",
  "published": "2017-11-30T20:09:46.000Z",
  "updated": "2017-11-30T20:09:46.000Z",
  "title": "Madness in vector spaces",
  "authors": [
    "Iian B. Smythe"
  ],
  "comment": "23 pages, 1 figure",
  "categories": [
    "math.LO"
  ],
  "abstract": "We consider maximal almost disjoint families of vector subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the \"spectrum\" of cardinalities of mad families of subspaces can be made arbitrarily large, in analogy to results for mad families on $\\omega$. We apply the author's local Ramsey theory for vector spaces to give partial results concerning their definability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-30T20:09:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E17",
      "03E15",
      "15A03"
    ],
    "keywords": [
      "mad families",
      "authors local ramsey theory",
      "minimum infinite cardinality",
      "partial results",
      "disjoint families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}