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

Journal of Mathematical Logic 22 (3) (2022)
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Abstract

Journal of Mathematical Logic, Volume 22, Issue 03, December 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 [math] 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 [math] to extensions of [math].

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B-frame duality.Guillaume Massas - 2023 - Annals of Pure and Applied Logic 174 (5):103245.

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