Spectral spaces are a class of topological spaces. They are a tool linking algebraic
structures, in a very wide sense, with geometry. They were invented to give a functional …

The standard topological representation of a Boolean algebra via the clopen sets of a Stone
space requires a nonconstructive choice principle, equivalent to the Boolean Prime Ideal …

In this thesis, we study positive (non-distributive) logics and their modal extensions by
means of duality theory. Our work is inspired by topological dualities for semilattices and …

In 1938, Tarski proved that a formula is not intuitionistically valid if, and only if, it has a
counter-model in the Heyting algebra of open sets of some topological space. In fact, Tarski …

The last decade has seen a surge of interest in nominal sets and their applications to formal
methods for programming languages. This thesis studies two subjects: algebra and duality …

Introducing Stone-Priestley duality theory and its applications to logic and theoretical
computer science, this book equips graduate students and researchers with the theoretical …

This paper introduces the category of b-frames as a new tool in the study of complete
lattices. B-frames can be seen as a generalization of posets, which play an important role in …

We develop a new duality for implicative semilattices, generalizing Esakia duality for Heyting
algebras. Our duality is a restricted version of generalized Priestley duality for distributive …

Abstract In [16], Esakia uses the Vietoris topology to give a coalgebra-flavored definition of
topological Kripke frames, thus relating the Vietoris topology, modal logic and coalgebra. In …

The Vietoris space of a Stone space plays an important role in the coalgebraic approach to
modal logic. When generalizing this to positive modal logic, there is a variety of relevant …