{
  "id": "1908.11145",
  "version": "v1",
  "published": "2019-08-29T10:46:21.000Z",
  "updated": "2019-08-29T10:46:21.000Z",
  "title": "Stationary Reflection and the failure of SCH",
  "authors": [
    "Omer Ben-Neria",
    "Yair Hayut",
    "Spencer Unger"
  ],
  "comment": "23 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper we prove that from large cardinals it is consistent that there is a singular strong limit cardinal $\\nu$ such that the singular cardinal hypothesis fails at $\\nu$ and every collection of fewer than $\\mathrm{cf}(\\nu)$ stationary subsets of $\\nu^+$ reflects simultaneously. For uncountable cofinality, this situation was not previously known to be consistent. Using different methods, we reduce the upper bound on the consistency strength of this situation for $\\mathrm{cf}(\\nu) = \\omega$ to below a single partially supercompact cardinal. The previous upper bound of infinitely many supercompact cardinals was due to Sharon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-29T10:46:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35"
    ],
    "keywords": [
      "stationary reflection",
      "upper bound",
      "singular strong limit cardinal",
      "singular cardinal hypothesis fails",
      "single partially supercompact cardinal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}