Dualities for Stone algebras, double Stone algebras, and relative Stone algebras
Endomorphisms of complete Heyting algebras.
Equationally close subframes and representation of quotient spaces
Equimorphy in varieties of double Heyting algebras
We show that any finitely generated variety V of double Heyting algebras is finitely determined, meaning that for some finite cardinal n(V), any class ⊆ V consisting of algebras with pairwise isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result complements the earlier established fact of categorical universality of the variety of all double Heyting algebras, and contrasts with categorical results concerning finitely generated varieties of distributive...
Fan-Gottesman type compactification of frames
Finite commutative monoids of open maps
Finitely axiomatizable varieties of BCK-algebras.
Gaps and dualities in Heyting categories
We present an algebraic treatment of the correspondence of gaps and dualities in partial ordered classes induced by the morphism structures of certain categories which we call Heyting (such are for instance all cartesian closed categories, but there are other important examples). This allows to extend the results of [14] to a wide range of more general structures. Also, we introduce a notion of combined dualities and discuss the relation of their structure to that of the plain ones.
Injectivity in the quasi-topo of separated presheaves on a complete Heyting algebra
Introduction de quelques formes générales des fonctions pseudo-booléennes.
Linear finitely separated objects of subcategories of domains
Local bounded commutative residuated -monoids
Bounded commutative residuated lattice ordered monoids (-monoids) are a common generalization of, e.g., -algebras and Heyting algebras. In the paper, the properties of local and perfect bounded commutative -monoids are investigated.
Logique, catégories et faisceaux
Measurable Refinement Monoids and Applications to Distributive Semilattices, Heyting Algebras, and Stone Spaces.
Modal extensions of Heyting algebras
Modal operators on symmetrical Heyting algebras
Natural continuity space structures on dual Heyting algebras
N-compact frames
We investigate notions of -compactness for frames. We find that the analogues of equivalent conditions defining -compact spaces are no longer equivalent in the frame context. Indeed, the closed quotients of frame ‘-cubes’ are exactly 0-dimensional Lindelöf frames, whereas those frames which satisfy a property based on the ultrafilter condition for spatial -compactness form a much larger class, and better embody what ‘-compact frames’ should be. This latter property is expressible without reference...
Note on dense covers in the category of locales
In this note we are going to study dense covers in the category of locales. We shall show that any product of finitely regular locales with some dense covering property has this property as well.
Notes on Kuratowski-Mrówka theorems in point-free context