{
  "id": "1507.04026",
  "version": "v1",
  "published": "2015-07-14T21:00:42.000Z",
  "updated": "2015-07-14T21:00:42.000Z",
  "title": "Generalized symmetric systems and thin-very tall compact scattered spaces",
  "authors": [
    "Miguel Angel Mota",
    "William Weiss"
  ],
  "comment": "14 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We solve a well--known problem in the theory of compact scattered spaces and superatomic boolean algebras by showing that, under GCH and for each regular cardinal $\\kappa \\geq \\omega$, there is a poset $\\mathcal P_\\kappa$ preserving all cardinals and forcing the existence of a $\\kappa$--thin very tall locally compact scattered space. For $\\kappa > \\omega$, we conceive the poset $\\mathcal P_\\kappa$ as a higher analogue of the poset $\\mathcal P_\\omega$ originally introduced by Asper\\'{o} and Bagaria in the context of an (unpublished) alternative consistency proof.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-14T21:00:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03G05",
      "54A25",
      "54A35",
      "54G12"
    ],
    "keywords": [
      "thin-very tall compact scattered spaces",
      "generalized symmetric systems",
      "superatomic boolean algebras",
      "tall locally compact scattered space",
      "well-known problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}