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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 extensions of [Formula: see text] to extensions of [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0219061322500131","type":"journal-article","created":{"date-parts":[[2022,6,22]],"date-time":"2022-06-22T09:27:13Z","timestamp":1655890033000},"source":"Crossref","is-referenced-by-count":2,"title":["A negative solution of Kuznetsov\u2019s problem for varieties of bi-Heyting algebras"],"prefix":"10.1142","volume":"22","author":[{"given":"Guram","family":"Bezhanishvili","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA"}]},{"given":"David","family":"Gabelaia","sequence":"additional","affiliation":[{"name":"Department of Mathematical Logic, TSU Razmadze Mathematical Institute, Tbilisi 0186, Georgia"}]},{"given":"Mamuka","family":"Jibladze","sequence":"additional","affiliation":[{"name":"Department of Mathematical Logic, TSU Razmadze Mathematical Institute, Tbilisi 0186, Georgia"}]}],"member":"219","published-online":{"date-parts":[[2022,6,22]]},"reference":[{"issue":"3","key":"S0219061322500131BIB001","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11083-008-9089-1","volume":"25","author":"Bezhanishvili G.","year":"2008","journal-title":"Order"},{"key":"S0219061322500131BIB002","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198537793.001.0001","volume-title":"Modal Logic","author":"Chagrov A.","year":"1997"},{"key":"S0219061322500131BIB003","first-page":"147","volume":"15","author":"Esakia L.","year":"1974","journal-title":"Soviet Math. 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