{
  "id": "math/0404151",
  "version": "v1",
  "published": "2004-04-07T04:52:31.000Z",
  "updated": "2004-04-07T04:52:31.000Z",
  "title": "Ladder gaps over stationary sets",
  "authors": [
    "Uri Abraham",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "For a stationary set S subseteq omega_1 and a ladder system C over S, a new type of gaps called C-Hausdorff is introduced and investigated. We describe a forcing model of ZFC in which, for some stationary set S, for every ladder C over S, every gap contains a subgap that is C-Hausdorff. But for every ladder E over omega_1 setminus S there exists a gap with no subgap that is E-Hausdorff. A new type of chain condition, called polarized chain condition, is introduced. We prove that the iteration with finite support of polarized c.c.c posets is again a polarized c.c.c poset.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-04-07T04:52:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary set",
      "ladder gaps",
      "polarized chain condition",
      "c-hausdorff",
      "finite support"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......4151A"
    }
  }
}