{
  "id": "1401.7948",
  "version": "v3",
  "published": "2014-01-30T18:31:26.000Z",
  "updated": "2014-05-04T01:50:29.000Z",
  "title": "A Lower Bound for Generalized Dominating Numbers",
  "authors": [
    "Dan Hathaway"
  ],
  "comment": "9 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show a new proof for the fact that when $\\kappa$ and $\\lambda$ are infinite cardinals satisfying $\\lambda ^ \\kappa = \\lambda$, the cofinality of the set of all functions from $\\lambda$ to $\\kappa$ ordered by everywhere domination is $2^\\lambda$. An earlier proof was a consequence of a result about independent families of functions. The new proof follows directly from the main theorem we present: for every $A \\subseteq \\lambda$ there is a function $f: {^\\kappa \\lambda} \\to \\kappa$ such that whenever $M$ is a transitive model of $\\textrm{ZF}$ such that ${^\\kappa \\lambda} \\subseteq M$ and some $g: {^\\kappa \\lambda} \\to \\kappa$ in $M$ dominates $f$, then $A \\in M$. That is, \"constructibility can be reduced to domination\".",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-05-04T01:50:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized dominating numbers",
      "lower bound",
      "domination",
      "earlier proof",
      "independent families"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.7948H"
    }
  }
}