{
  "id": "1802.07986",
  "version": "v1",
  "published": "2018-02-22T11:36:06.000Z",
  "updated": "2018-02-22T11:36:06.000Z",
  "title": "A Version of $κ$-Miller Forcing",
  "authors": [
    "Heike Mildenberger",
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $\\kappa$ be a regular uncountable cardinal such that $2^{<\\kappa} = \\kappa$ or just $2^{(\\kappa^{<\\kappa})} = 2^\\kappa$ and there is a $\\kappa$-mad family of size $2^\\kappa$. We show under these assumptions the forcing order $\\kappa$-Miller with club many splitting nodes collapses $2^\\kappa$ to $\\omega$ and adds a $\\kappa$-Cohen real.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-22T11:36:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E17",
      "03E35"
    ],
    "keywords": [
      "miller forcing",
      "regular uncountable cardinal",
      "splitting nodes collapses",
      "cohen real",
      "assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}