{
  "id": "1808.09088",
  "version": "v1",
  "published": "2018-08-28T01:58:36.000Z",
  "updated": "2018-08-28T01:58:36.000Z",
  "title": "Combinatorics of Borel Ideals",
  "authors": [
    "José de Jesús Pelayo Gómez"
  ],
  "comment": "28 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "In this work we study some combinatorial properties of Borel (or co-analytic) ideals on countable sets. We shall extend the theorem 4.18 presented in \\cite{articulomaicol}, and also we will find an $F_\\sigma$ tall ideal in which the player $II$ has a winning stratagy in the \\emph{Cut and Choose Game} which was a question of J. Zapletal. In the second section some Ramsey properties of ideals are presented, for example it was known that the random graph ideal is critical for the Ramsey property (for subsets of size two and colorings with two colors) and we construct a critical ideal for every Ramsey property. The third section contains some comments of the Solecki ideal and finally in the forth section it is found an $F_\\sigma$ tall $K$-uniform ideal not equivalent with $\\mathcal{ ED }_{fin}$ (question 5.11, \\cite{michaeldiagrama} due to Michael Hru\\v{s}\\'ak).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-28T01:58:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E17",
      "03E05",
      "03E35"
    ],
    "keywords": [
      "borel ideals",
      "ramsey property",
      "combinatorics",
      "random graph ideal",
      "third section contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}