A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras
Logic
2021-04-14 v1
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 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 .
Keywords
Cite
@article{arxiv.2104.05961,
title = {A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras},
author = {Guram Bezhanishvili and David Gabelaia and Mamuka Jibladze},
journal= {arXiv preprint arXiv:2104.05961},
year = {2021}
}