{
  "id": "2009.03471",
  "version": "v1",
  "published": "2020-09-08T01:02:44.000Z",
  "updated": "2020-09-08T01:02:44.000Z",
  "title": "Borel sets without perfectly many overlapping translations, III",
  "authors": [
    "Andrzej Roslanowski",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We expand the results of Roslanowski and Shelah arXive:1806.06283 , arXive:1909.00937 to all perfect Abelian Polish groups $(H,+)$. In particular, we show that if $\\alpha<\\omega_1$ and $4\\leq k<\\omega$, then there is a ccc forcing notion adding a $\\Sigma^0_2$ set $B\\subseteq H$ which has $\\aleph_\\alpha$ many pairwise $k$--overlapping translations but not a perfect set of such translations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-08T01:02:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E15",
      "03E50"
    ],
    "keywords": [
      "overlapping translations",
      "borel sets",
      "perfect abelian polish groups",
      "perfect set",
      "roslanowski"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}