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arXiv · 2104.05961

A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras

Guram Bezhanishvili·David Gabelaia·Mamuka Jibladze
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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 $\mathsf{HB}$.

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Guram Bezhanishvili, David Gabelaia, Mamuka Jibladze. 2021-04-13. A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras. https://arxiv.org/abs/2104.05961

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