{
  "id": "0805.2031",
  "version": "v1",
  "published": "2008-05-14T11:21:27.000Z",
  "updated": "2008-05-14T11:21:27.000Z",
  "title": "On filling families of finite subsets of the Cantor set",
  "authors": [
    "Pandelis Dodos",
    "Vassilis Kanellopoulos"
  ],
  "comment": "14 pages, no figures. Mathematical Proceedings of the Cambridge Philosophical Society (to appear)",
  "journal": "Mathematical Proceedings of the Cambridge Phil. Society 145 (2008), 165-175",
  "categories": [
    "math.LO",
    "math.CO"
  ],
  "abstract": "Let $\\ee>0$ and $\\fff$ be a family of finite subsets of the Cantor set $\\ccc$. Following D. H. Fremlin, we say that $\\fff$ is $\\ee$-filling over $\\ccc$ if $\\fff$ is hereditary and for every $F\\subseteq\\ccc$ finite there exists $G\\subseteq F$ such that $G\\in\\fff$ and $|G|\\geq\\ee |F|$. We show that if $\\fff$ is $\\ee$-filling over $\\ccc$ and $C$-measurable in $[\\ccc]^{<\\omega}$, then for every $P\\subseteq\\ccc$ perfect there exists $Q\\subseteq P$ perfect with $[Q]^{<\\omega}\\subseteq\\fff$. A similar result for weaker versions of density is also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-14T11:21:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "05D10",
      "46B15"
    ],
    "keywords": [
      "finite subsets",
      "cantor set",
      "filling families",
      "similar result"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.2031D"
    }
  }
}