{
  "id": "1903.10476",
  "version": "v1",
  "published": "2019-03-25T17:23:03.000Z",
  "updated": "2019-03-25T17:23:03.000Z",
  "title": "Guessing models imply the singular cardinal hypothesis",
  "authors": [
    "John Krueger"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this article we prove three main theorems: (1) guessing models are internally unbounded, (2) for any regular cardinal $\\kappa \\ge \\omega_2$, $\\textsf{ISP}(\\kappa)$ implies that $\\textsf{SCH}$ holds above $\\kappa$, and (3) forcing posets which have the $\\omega_1$-approximation property also have the countable covering property. These results solve open problems of Viale and Hachtman-Sinapova.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-25T17:23:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05"
    ],
    "keywords": [
      "singular cardinal hypothesis",
      "guessing models",
      "regular cardinal",
      "main theorems",
      "approximation property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}