In traditional semantics for classical logic and its extensions, such as modal logic,
propositions are interpreted as subsets of a set, as in discrete duality, or as clopen sets of a …

For a frame L, let XL be the Esakia space of L. We identify a special subset YL of XL
consisting of nuclear points of XL, and prove the following results:• L is spatial iff YL is dense …

McKinsey and Tarski initiated the study of interior algebras. We propose complete interior
algebras as an alternative pointfree approach to topology. We term these algebras …

There are several prominent duality results in pointfree topology. Hofmann–Lawson duality
establishes that the category of continuous frames is dually equivalent to the category of …

In this paper we shall study some classes of bounded distributive lattices endowed with a
subordination relation, called subordination lattices. We shall prove that certain algebraic …

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Let OS OS be the frame of open sets of a topological space S, and let N (OS) N(OS) be the
frame of nuclei on OS OS. For an Alexandroff space S, we prove that N (OS) N(OS) is spatial …

We utilize the Bruns-Lakser completion to introduce Bruns-Lakser towers of a meet-
semilattice. This machinery enables us to develop various hierarchies inside the class of …

We show how up-to techniques for (bi-) similarity can be used in the setting of weighted
systems. The problems we consider are language equivalence, language inclusion and the …

We introduce proximity morphisms between MT-algebras and show that the resulting
category is equivalent to the category of frames. This is done by utilizing the Funayama …