{
  "id": "1808.05930",
  "version": "v1",
  "published": "2018-08-17T17:02:00.000Z",
  "updated": "2018-08-17T17:02:00.000Z",
  "title": "Free sequences in P(ω)/fin",
  "authors": [
    "David Chodounský",
    "Vera Fischer",
    "Jan Grebík"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate maximal free sequences in the Boolean algebra $\\mathcal{P}(\\omega)/\\mathrm{fin}$, as defined by D. Monk. We provide some information on the general structure of these objects and we are particularly interested in the minimal cardinality of a free sequence, a cardinal characteristic of the continuum denoted $\\mathfrak{f}$. Answering a question of Monk, we demonstrate the consistency of $\\omega_1 = \\mathfrak{i} = \\mathfrak{f} < \\mathfrak{u} = \\omega_2$. In fact, this consistency is demonstrated in the model of S. Shelah for $\\mathfrak{i} < \\mathfrak{u}$. Our paper provides a streamlined and mostly self contained presentation of this construction.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-17T17:02:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E17",
      "03E35",
      "06E05"
    ],
    "keywords": [
      "maximal free sequences",
      "boolean algebra",
      "general structure",
      "minimal cardinality",
      "cardinal characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}