{
  "id": "math/9911225",
  "version": "v1",
  "published": "1999-11-28T00:45:12.000Z",
  "updated": "1999-11-28T00:45:12.000Z",
  "title": "On cardinalities in quotients of inverse limits of groups",
  "authors": [
    "Rami Grossberg",
    "Saharon Shelah"
  ],
  "journal": "Mathematica Japonica, 47(1998):189-197",
  "categories": [
    "math.LO"
  ],
  "abstract": "Let lambda be aleph_0 or a strong limit of cofinality aleph_0. Suppose that (G_m,p_{m,n}:m =< n<omega) and (H_m,p^t_{m,n}: m=< n < omega) are projective systems of groups of cardinality less than lambda and suppose that for every n<omega there is a homomorphism h:H_n-->G_n such that all the diagrams commute. If for every mu<lambda there exists (f_i in G_omega:i<mu) such that for distinct i,j we have: f_i f_j^{-1} notin h_omega(H_omega), then there exists (f_i in G_omega:i<2^lambda) such that for distinct i,j we have f_i f_j^{-1} notin h_omega(H_omega).",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-11-28T00:45:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "inverse limits",
      "cardinalities",
      "strong limit",
      "diagrams commute"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....11225G"
    }
  }
}