{
  "id": "math/9702206",
  "version": "v1",
  "published": "1997-02-18T00:00:00.000Z",
  "updated": "1997-02-18T00:00:00.000Z",
  "title": "The maximality of the core model",
  "authors": [
    "Ernest Schimmerling",
    "John R. Steel"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of maximality are proved, including: o K computes successors of weakly compact cardinals correctly. o K^c is an iterate of K. o (with Mitchell) If alpha is a cardinal > aleph_1, then K-restriction-alpha is universal for mice of height alpha. Other results in this paper, when combined with work of Woodin, imply: o If square-kappa-finite fails and kappa is a singular, strong limit cardinal, then Inductive Determinacy holds. o If square-kappa-finite fails and kappa is a weakly compact cardinal, then L(R)-determinacy holds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-02-18T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "core model",
      "maximality",
      "weakly compact cardinal",
      "square-kappa-finite fails",
      "final model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1997math......2206S"
    }
  }
}