{
  "id": "1811.05444",
  "version": "v1",
  "published": "2018-11-13T18:23:56.000Z",
  "updated": "2018-11-13T18:23:56.000Z",
  "title": "Cardinal Characteristics of Models of Set Theory",
  "authors": [
    "Douglas Ulrich"
  ],
  "comment": "35 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We continue our investigation =of Shelah's interpretability orders $\\trianglelefteq^*_\\kappa$ as well as the new orders $\\trianglelefteq^\\times_\\kappa$. In particular, we give streamlined proofs of the existence of minimal unstable, unsimple and nonlow theories in these orders, and we give a similar analysis of the hypergraph examples $T_{n, k}$ of Hrushovski. We also prove that if $\\mathcal{B}$ is a complete Boolean algebra with the $\\lambda$-c.c., then no nonprincipal ultrafilter on $\\mathcal{U}$ $\\lambda^+$-saturates any unsimple theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-13T18:23:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C55"
    ],
    "keywords": [
      "set theory",
      "cardinal characteristics",
      "complete boolean algebra",
      "shelahs interpretability orders",
      "nonprincipal ultrafilter"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}