{
  "id": "1909.08078",
  "version": "v1",
  "published": "2019-09-17T20:22:09.000Z",
  "updated": "2019-09-17T20:22:09.000Z",
  "title": "Mad families of vector subspaces and the smallest nonmeager set of reals",
  "authors": [
    "Iian B. Smythe"
  ],
  "comment": "8 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that a parametrized $\\diamondsuit$ principle, corresponding to the uniformity of the meager ideal, implies that the minimum cardinality of an infinite maximal almost disjoint family of block subspaces in a countable vector space is $\\aleph_1$. Consequently, this cardinal invariant is $\\aleph_1$ in the Miller model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-17T20:22:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E17",
      "15A03"
    ],
    "keywords": [
      "smallest nonmeager set",
      "mad families",
      "vector subspaces",
      "cardinal invariant",
      "meager ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}