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A negative solution of Kuznetsov's problem for varieties of bi-Heyting algebras
Guram Bezhanishvili, David Gabelaia, Mamuka Jibladze
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…
Diego's Theorem for nuclear implicative semilattices
Guram Bezhanishvili, Nick Bezhanishvili, Luca Carai +3
We prove that the variety of nuclear implicative semilattices is locally finite, thus generalizing Diego's Theorem. The key ingredients of our proof include the coloring technique…
Modal logic of planar polygons
David Gabelaia, Kristina Gogoladze, Mamuka Jibladze +2
We study the modal logic of the closure algebra , generated by the set of all polygons in the Euclidean plane . We show that this logic is finitely axiomatizable…
Topological interpretations of provability logic
Lev Beklemishev, David Gabelaia
Provability logic concerns the study of modality as provability in formal systems such as Peano arithmetic. Natural, albeit quite surprising, topological interpretation of p…
Modal languages for topology: expressivity and definability
Balder ten Cate, David Gabelaia, Dmitry Sustretov
In this paper we study the expressive power and definability for (extended) modal languages interpreted on topological spaces. We provide topological analogues of the van Benthem c…