{
  "id": "2104.05961",
  "version": "v1",
  "published": "2021-04-13T06:30:48.000Z",
  "updated": "2021-04-13T06:30:48.000Z",
  "title": "A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras",
  "authors": [
    "Guram Bezhanishvili",
    "David Gabelaia",
    "Mamuka Jibladze"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that there exist (continuum many) varieties of bi-Heyting algebras that are not generated by their complete members. It follows that there exist (continuum many) extensions of the Heyting-Brouwer logic $\\mathsf{HB}$ that are topologically incomplete. This result provides further insight into the long-standing open problem of Kuznetsov by yielding a negative solution of the reformulation of the problem from intermediate logics to extensions of $\\mathsf{HB}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-13T06:30:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03B55",
      "06D20",
      "06D22",
      "03B45",
      "06E15"
    ],
    "keywords": [
      "bi-heyting algebras",
      "negative solution",
      "kuznetsovs problem",
      "intermediate logics",
      "complete members"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}