{
  "id": "1810.08702",
  "version": "v1",
  "published": "2018-10-19T22:24:07.000Z",
  "updated": "2018-10-19T22:24:07.000Z",
  "title": "Inner mantles and iterated HOD",
  "authors": [
    "Jonas Reitz",
    "Kameryn J Williams"
  ],
  "comment": "17 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We present a class forcing notion $\\mathbb M(\\eta)$, uniformly definable for ordinals $\\eta$, which forces the ground model to be the $\\eta$-th inner mantle of the extension, in which the sequence of inner mantles has length at least $\\eta$. This answers a conjecture of Fuchs, Hamkins, and Reitz [FHR15] in the positive. We also show that $\\mathbb M(\\eta)$ forces the ground model to be the $\\eta$-th iterated HOD of the extension, where the sequence of iterated HODs has length at least $\\eta$. We conclude by showing that the lengths of the sequences of inner mantles and of iterated HODs can be separated to be any two ordinals you please.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-19T22:24:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E40"
    ],
    "keywords": [
      "ground model",
      "th inner mantle",
      "class forcing notion",
      "th iterated hod",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}