{
  "id": "math/9603219",
  "version": "v1",
  "published": "1996-03-15T00:00:00.000Z",
  "updated": "1996-03-15T00:00:00.000Z",
  "title": "The consistency of 2^{aleph_{0}}> aleph_{omega} + I(aleph_{2})=I(aleph_{omega})",
  "authors": [
    "Martin Gilchrist",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "An omega-coloring is a pair <f,B> where f:[B]^{2} ---> omega. The set B is the field of f and denoted Fld(f). Let f,g be omega-colorings. We say that f realizes the coloring g if there is a one-one function k:Fld(g) ---> Fld(f) such that for all {x,y}, {u,v} in dom(g) we have f({k(x),k(y)}) not= f({k(u),k(v)}) => g({x,y}) not= g({u,v}). We write f~g if f realizes g and g realizes f. We call the ~-classes of omega-colorings with finite fields identities. We say that an identity I is of size r if |Fld(f)|=r for some/all f in I. For a cardinal kappa and f:[kappa]^2 ---> omega we define I(f) to be the collection of identities realized by f and I (kappa) to be bigcap {I(f)| f:[kappa]^2 ---> omega}. We show that, if ZFC is consistent then ZFC + 2^{aleph_0}> aleph_omega + I(aleph_2)=I(aleph_omega) is consistent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-03-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "consistency",
      "finite fields identities",
      "cardinal kappa",
      "consistent",
      "one-one function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1996math......3219G"
    }
  }
}