5 papers
The pairwise Stone space of an S4 De Morgan algebra
Joseph McDonald, Filip Jankovec
The purpose of this study is to investigate the bitopological duality theory of De Morgan algebras equipped with a closure operator, known as S4 De Morgan algebras. We first introd…
Monadic and cylindric expansions of bounded implication algebras
Joseph McDonald
Implication algebras were introduced by Abbott as algebraic models of the operation of Boolean implication in the classical propositional calculus. In this work, we study additiona…
Spectral duality for some modal and residuated groupoid expansions of De Morgan algebras
Joseph McDonald
Stone demonstrated that the category of bounded distributive lattices is dually equivalent to the category of spectral spaces and Priestley s…
Cylindric quasi-implication algebras
Joseph McDonald
In this note, we study the operation of Sasaki hook within the setting of quantum cylindric algebras by introducing cylindric quasi-implication algebras. It is first demonstrated t…
Canonical completion and duality for cylindric ortholattices and cylindric Boolean algebras
Joseph McDonald
In this note, we investigate the algebraic and topological representation theory of cylindric ortholattices and cylindric Boolean algebras. The first contribution demonstrates that…