{
  "id": "math/9808056",
  "version": "v1",
  "published": "1998-08-12T22:13:42.000Z",
  "updated": "1998-08-12T22:13:42.000Z",
  "title": "More on cardinal invariants of Boolean algebras",
  "authors": [
    "Andrzej Roslanowski",
    "Saharon Shelah"
  ],
  "comment": "accepted for Annals of Pure and Applied Logic",
  "journal": "Ann. Pure Appl. Logic 103 (2000) 1-37",
  "categories": [
    "math.LO",
    "math.GN",
    "math.RA"
  ],
  "abstract": "We address several questions of Donald Monk related to irredundance and spread of Boolean algebras, gaining both some ZFC knowledge and consistency results. We show in ZFC that irr(B_0 times B_1)= max(irr(B_0),irr(B_1)). We prove consistency of the statement ``there is a Boolean algebra B such that irr(B)<s(B otimes B)'' and we force a superatomic Boolean algebra B_* such that s(B_*)=inc(B_*)=kappa, irr(B_*)=Id(B_*)=kappa^+ and Sub(B_*)=2^(kappa^+). Next we force a superatomic algebra B_0 such that irr(B_0)<inc(B_0) and a superatomic algebra B_1 such that t(B_1)>Aut(B_1). Finally we show that consistently there is a Boolean algebra B of size lambda such that there is no free sequence in B of length lambda, there is an ultrafilter of tightness lambda (so t(B)=lambda) and lambda notin Depth_(Hs)(B).",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-08-12T22:13:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "06Exx",
      "54A25"
    ],
    "keywords": [
      "boolean algebra",
      "cardinal invariants",
      "consistency results",
      "zfc knowledge",
      "free sequence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......8056R"
    }
  }
}