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

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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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10.1142/s0219061322500131

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Citations of this work

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

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References found in this work

Heyting Algebras: Duality Theory.Leo Esakia - 2019 - Cham, Switzerland: Springer Verlag.
Modal Logic.Yde Venema, Alexander Chagrov & Michael Zakharyaschev - 2000 - Philosophical Review 109 (2):286.
An incomplete logic containing S.Kit Fine - 1974 - Theoria 40 (1):23-29.

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