{
  "id": "1211.3350",
  "version": "v3",
  "published": "2012-11-14T16:28:09.000Z",
  "updated": "2013-03-03T18:18:54.000Z",
  "title": "Base Tree Property",
  "authors": [
    "Bohuslav Balcar",
    "Michal Doucha",
    "Michael Hrušák"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Building on previous work of [BPS] we investigate $\\sigma$-closed partial orders of size continuum. We provide both an internal and external characterization of such partial orders by showing that (1) every $\\sigma$-closed partial order of size continuum has a base tree and that (2) $\\sigma$-closed forcing notions of density $\\mathfrak c$ correspond exactly to regular suborders of the collapsing algebra $Coll(\\omega_1, 2^\\omega)$. We further study some naturally ocurring examples of such partial orders.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-03-03T18:18:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "base tree property",
      "closed partial order",
      "size continuum",
      "external characterization",
      "regular suborders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.3350B"
    }
  }
}