A negative solution of Kuznetsov’s problem for varieties of bi-Heyting algebras
Guram Bezhanishvili, David Gabelaia, Mamuka Jibladze · Journal of Mathematical Logic · 2022
In this paper, 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 [Formula: see text] 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 extensions of [Formula: see text] to extensions of [Formula: see text].