{
  "id": "math/9801154",
  "version": "v1",
  "published": "1998-01-15T00:00:00.000Z",
  "updated": "1998-01-15T00:00:00.000Z",
  "title": "A model with no magic sets",
  "authors": [
    "Krzysztof Ciesielski",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We will prove that there exists a model of ZFC+``c= omega_2'' in which every M subseteq R of cardinality less than continuum c is meager, and such that for every X subseteq R of cardinality c there exists a continuous function f:R-> R with f[X]=[0,1]. In particular in this model there is no magic set, i.e., a set M subseteq R such that the equation f[M]=g[M] implies f=g for every continuous nowhere constant functions f,g:R-> R .",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-01-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "magic set",
      "cardinality",
      "constant functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......1154C"
    }
  }
}