English

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 HB\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 HB\mathsf{HB}.

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}
}