{
  "id": "1903.03170",
  "version": "v1",
  "published": "2019-03-07T20:21:08.000Z",
  "updated": "2019-03-07T20:21:08.000Z",
  "title": "Finite powers and products of Menger sets",
  "authors": [
    "Piotr Szewczak",
    "Boaz Tsaban",
    "Lyubomyr Zdomskyy"
  ],
  "comment": "14 pages",
  "categories": [
    "math.GN",
    "math.LO"
  ],
  "abstract": "We construct, using mild combinatorial hypotheses, a real Menger set that is not Scheepers, and two real sets that are Menger in all finite powers, with a non-Menger product. By a forcing-theoretic argument, we show that the same holds in the Blass--Shelah model for arbitrary values of the ultrafilter and dominating number.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-07T20:21:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "54D20",
      "03E17"
    ],
    "keywords": [
      "finite powers",
      "mild combinatorial hypotheses",
      "real menger set",
      "arbitrary values",
      "blass-shelah model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}