{
  "id": "1604.06044",
  "version": "v1",
  "published": "2016-04-20T18:00:57.000Z",
  "updated": "2016-04-20T18:00:57.000Z",
  "title": "On cuts in ultraproducts of linear orders II",
  "authors": [
    "Mohammad Golshani",
    "Saharon Shelah"
  ],
  "comment": "This is publication 1087 of second author",
  "categories": [
    "math.LO"
  ],
  "abstract": "We continue our study of the class $\\mathscr{C}(D)$, where $D$ is a uniform ultrafilter on a cardinal $\\kappa$ and $\\mathscr{C}(D)$ is the class of all pairs $(\\theta_1, \\theta_2),$ where $(\\theta_1, \\theta_2)$ is the cofinality of a cut in $J^\\kappa /D$ and $J$ is some $(\\theta_1+\\theta_2)^+$-saturated dense linear order. We give a combinatorial characterization of the class $\\mathscr{C}(D)$. We also show that if $(\\theta_1, \\theta_2) \\in \\mathscr{C}(D)$ and $D$ is $\\aleph_1$-complete or $\\theta_1 + \\theta_2 > 2^\\kappa,$ then $\\theta_1=\\theta_2.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-20T18:00:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "ultraproducts",
      "saturated dense linear order",
      "uniform ultrafilter",
      "combinatorial characterization",
      "cofinality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160406044G"
    }
  }
}