{
  "id": "2402.04065",
  "version": "v1",
  "published": "2024-02-06T15:10:26.000Z",
  "updated": "2024-02-06T15:10:26.000Z",
  "title": "Mice with Woodin cardinals from a Reinhardt",
  "authors": [
    "Farmer Schlutzenberg"
  ],
  "comment": "12 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Suppose there is a Reinhardt cardinal. Then (1) $M_n(X)$ exists and is fully iterable (above $X$) for every transitive set $X$ and every $n<\\omega$ (here $M_n(X)$ denotes the canonical minimal proper class inner model containing $X$ and having $n$ Woodin cardinals above the rank of $X$); and (2) Projective Determinacy holds in every set generic extension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-06T15:10:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E55",
      "03E45",
      "03E25",
      "03E60"
    ],
    "keywords": [
      "woodin cardinals",
      "minimal proper class inner model",
      "canonical minimal proper class inner",
      "set generic extension",
      "proper class inner model containing"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}