{
  "id": "1004.4798",
  "version": "v1",
  "published": "2010-04-27T13:34:03.000Z",
  "updated": "2010-04-27T13:34:03.000Z",
  "title": "Superatomic Boolean algebras constructed from strongly unbounded functions",
  "authors": [
    "Juan Carlos Martinez",
    "Lajos Soukup"
  ],
  "comment": "13 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that $\\kappa,\\lambda$ are infinite cardinals such that $\\kappa^{+++} \\leq \\lambda$, $\\kappa^{<\\kappa}=\\kappa$ and $2^{\\kappa}= \\kappa^+$, and $\\eta$ is an ordinal with $\\kappa^+\\leq \\eta <\\kappa^{++}$ and $cf(\\eta) = \\kappa^+$. Then, in some cardinal-preserving generic extension there is a superatomic Boolean algebra $B$ such that - $ht(B) = \\eta + 1$, - the cardinality of the $\\alpha$th level of $B$ is $\\kappa$ for every $\\alpha <\\eta$, - and the cardinality of the $\\eta$th level of $B$ is $\\lambda$ Especially, $\\<{\\omega}\\>_{{\\omega}_1}\\concatenation \\<{\\omega}_3\\>$ and $\\<{\\omega}_1\\>_{{\\omega}_2}\\concatenation \\<{\\omega}_4\\>$ can be cardinal sequences of superatomic Boolean algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-04-27T13:34:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "06E05",
      "54A25",
      "54G12"
    ],
    "keywords": [
      "superatomic boolean algebras",
      "th level",
      "cardinal-preserving generic extension",
      "koszmiders strongly unbounded functions",
      "cardinal sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.4798M"
    }
  }
}