{
  "id": "1806.06283",
  "version": "v1",
  "published": "2018-06-16T19:22:54.000Z",
  "updated": "2018-06-16T19:22:54.000Z",
  "title": "Borel sets without perfectly many overlapping translations",
  "authors": [
    "Andrzej Roslanowski",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "For a cardinal lambda<lambda_{omega_1} we give a ccc forcing notion P which forces that for some Borel subset B of the Cantor space (1) there a sequence (eta_alpha:alpha<lambda) of distinct elements such that |(eta_alpha+B) cap (eta_beta+B)|>5 for all alpha,beta<lambda, but (2) there is no perfect set of such eta's. The construction closely follows the one from Shelah math.LO/9802134",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-16T19:22:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "borel sets",
      "overlapping translations",
      "cardinal lambda",
      "perfect set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}