{
  "id": "1607.03291",
  "version": "v1",
  "published": "2016-07-12T10:03:45.000Z",
  "updated": "2016-07-12T10:03:45.000Z",
  "title": "Free sets for a set-mapping relative to a family of sets",
  "authors": [
    "Antonio Avilés",
    "Claribet Piña"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Given a family $\\mathcal{F}$ of subsets of $\\{1,\\ldots,m\\}$, we try to compute the least natural number $n$ such that for every function $S:[\\aleph_n]^{<\\omega}\\longrightarrow [\\aleph_n]^{<\\omega}$ there exists a bijection $u:\\{1,\\ldots,m\\}\\longrightarrow Y\\subset \\aleph_n$ such that $Su(A)\\cap Y \\subset u(A)$ for all $A\\in\\mathcal{F}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-12T10:03:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free sets",
      "set-mapping relative",
      "natural number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}