We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of
logics algebraically captured by varieties of normal and regular lattice expansions. This …

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 …

In this chapter we survey some recent developments in duality for lattices with additional
operations paying special attention to Heyting algebras and the connections to Esakia's …

Jónsson and Tarski's notion of the perfect extension of a Boolean algebra with operators has
evolved into an extensive theory of canonical extensions of lattice-based algebras. After …

Many results in logic and mathematics rely on techniques that allow for concrete, often
visual, representations of abstract concepts. A primary example of this phenomenon in logic …

Recently W. Holliday gave a choice-free construction of a canonical extension of a boolean
algebra B as the boolean algebra of regular open subsets of the Alexandroff topology on the …

Sahlqvist theory is extended to the fragments of the intuitionistic propositional calculus that
include the conjunction connective. This allows us to introduce a Sahlqvist theory of …

On Hilbert algebras generated by the order | Archive for Mathematical Logic Skip to main
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In this thesis, we study various generalizations and weakenings of the Rasiowa-Sikorski
Lemma (Rasiowa-Sikorski [55]) for Boolean algebras. Building on previous work from …

The aim of this article is to propose an adequate completion for distributive nearlattices. We
give a proof of the existence of such a completion through a representation theorem, which …