2021/04/13 by Bezhanishvili, Guram, Gabelaia, David, Jibladze, Mamuka
#03B45 #03B55 #06D20 #06D22 #06E15 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2104.05961
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 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.