{
  "id": "1708.02814",
  "version": "v1",
  "published": "2017-08-09T12:38:36.000Z",
  "updated": "2017-08-09T12:38:36.000Z",
  "title": "On large cardinals and generalized Baire spaces",
  "authors": [
    "David Asperó",
    "Tapani Hyttinen",
    "Vadim Kulikov",
    "Miguel Moreno"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Working under large cardinal assumptions, we study the Borel-reducibility between equivalence relations modulo restrictions of the non-stationary ideal on some fixed cardinal $\\kappa$. We show the consistency of $E^{\\lambda^{++},\\lambda^{++}}_{\\lambda\\text{-club}}$, the relation of equivalence modulo the non-stationary ideal restricted to $S^{\\lambda^{++}}_\\lambda$ in the space $(\\lambda^{++})^{\\lambda^{++}}$, being continuously reducible to $E^{2,\\lambda^{++}}_{\\lambda^+\\text{-club}}$, the relation of equivalence modulo the non-stationary ideal restricted to $S^{\\lambda^{++}}_{\\lambda^+}$ in the space $2^{\\lambda^{++}}$. Then we show the consistency of $E^{2,\\kappa}_{reg}$, the relation of equivalence modulo the non-stationary ideal restricted to regular cardinals in the space $2^{\\kappa}$, being $\\Sigma_1^1$-complete. We finish by showing, for $\\Pi_2^1$-indescribable $\\kappa$, that the isomorphism relation between dense linear orders of cardinality $\\kappa$ is $\\Sigma_1^1$-complete.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-09T12:38:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized baire spaces",
      "non-stationary ideal",
      "equivalence modulo",
      "equivalence relations modulo restrictions",
      "large cardinal assumptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}