{
  "id": "2003.02238",
  "version": "v1",
  "published": "2020-03-04T18:25:45.000Z",
  "updated": "2020-03-04T18:25:45.000Z",
  "title": "Equivalence Relations and Determinacy",
  "authors": [
    "Logan Crone",
    "Lior Fishman",
    "Stephen Jackson"
  ],
  "comment": "13 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We introduce the notion of $(\\Gamma,E)$-determinacy for $\\Gamma$ a pointclass and $E$ an equivalence relation on a Polish space $X$. A case of particular interest is the case when $E=E_G$ is the (left) shift-action of $G$ on $S^G$ where $S=2=\\{0,1\\}$ or $S=\\omega$. We show that for all shift actions by countable groups $G$, and any \"reasonable\" pointclass $\\Gamma$, that $(\\Gamma,E_G)$-determinacy implies $\\Gamma$-determinacy. We also prove a corresponding result when $E$ is a subshift of finite type of the shift map on $2^\\mathbb{Z}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-04T18:25:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E60"
    ],
    "keywords": [
      "equivalence relation",
      "shift actions",
      "shift map",
      "finite type",
      "determinacy implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}