{
  "id": "math/9812114",
  "version": "v1",
  "published": "1998-12-18T17:31:12.000Z",
  "updated": "1998-12-18T17:31:12.000Z",
  "title": "Strongly almost disjoint families, II",
  "authors": [
    "Andras Hajnal",
    "Istvan Juhasz",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "The relations M(kappa,lambda,mu)->B [resp. B(sigma)] meaning that if A subset [kappa]^lambda with |A|=kappa is mu-almost disjoint then A has property B [resp. has a sigma-transversal] had been introduced and studied under GCH by Erdos and Hajnal in 1961. Our two main results here say the following: Assume GCH and rho be any regular cardinal with a supercompact [resp. 2-huge] cardinal above rho. Then there is a rho-closed forcing P such that, in V^P, we have both GCH and M(rho^{(+rho+1)},rho^+,rho) not-> B [resp. M(rho^{(+rho+1)},lambda,rho) not-> B(rho^+) for all lambda =< rho^{(+rho+1)}].",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-12-18T17:31:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E35",
      "03E55",
      "04A20",
      "04A30"
    ],
    "keywords": [
      "disjoint families",
      "mu-almost disjoint",
      "main results",
      "assume gch",
      "regular cardinal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....12114H"
    }
  }
}