{
  "id": "math/0405473",
  "version": "v1",
  "published": "2004-05-25T17:50:38.000Z",
  "updated": "2004-05-25T17:50:38.000Z",
  "title": "The cardinal characteristic for relative gamma-sets",
  "authors": [
    "Arnold W. Miller"
  ],
  "categories": [
    "math.LO",
    "math.GN"
  ],
  "abstract": "For $X$ a separable metric space define $\\pp(X)$ to be the smallest cardinality of a subset $Z$ of $X$ which is not a relative $\\ga$-set in $X$, i.e., there exists an $\\om$-cover of $X$ with no $\\ga$-subcover of $Z$. We give a characterization of $\\pp(2^\\om)$ and $\\pp(\\om^\\om)$ in terms of definable free filters on $\\om$ which is related to the psuedointersection number $\\pp$. We show that for every uncountable standard analytic space $X$ that either $\\pp(X)=\\pp(2^\\om)$ or $\\pp(X)=\\pp(\\om^\\om)$. We show that both of following statements are each relatively consistent with ZFC: (a) $\\pp=\\pp(\\om^\\om) < \\pp(2^\\om)$ and (b) $\\pp < \\pp(\\om^\\om) =\\pp(2^\\om)$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-25T17:50:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "54D20",
      "03E50"
    ],
    "keywords": [
      "cardinal characteristic",
      "relative gamma-sets",
      "separable metric space define",
      "uncountable standard analytic space",
      "smallest cardinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5473M"
    }
  }
}