Configurations in Coproducts of Priestley Spaces

Configurations in Coproducts of Priestley Spaces

More on Configurations in Priestley Spaces, and Some New Problems

Prohibiting configurations (≡ induced finite connected posets) in Priestley spaces and properties of the associated classes of distributive lattices, and the related problem of configurations in coproducts of Priestley spaces, have been brought to satisfactory conclusions in case of configurations with a unique maximal element. The general case is, however, far from settled. After a short surve...

Priestley Configurations and Heyting Varieties

We investigate Heyting varieties determined by prohibition of systems of configuraations in Priestley duals; we characterize the configuration systems yielding such varieties. On the other hand, the question whether a given finitely generated Heyting variety is obtainable by such means is solved for the special case of systems of trees. Priestley duality provides a correspondence between bounde...

Coproducts of Distributive Lattice based Algebras

The analysis of coproducts in varieties of algebras has generally been variety-specific, relying on tools tailored to particular classes of algebras. A recurring theme, however, is the use of a categorical duality. Among the dualities and topological representations in the literature, natural dualities are particularly well behaved with respect to coproduct. Since (multisorted) natural dualitie...

Tame Parts of Free Summands in Coproducts of Priestley Spaces

It is well known that a sum (coproduct) of a family {Xi : i ∈ I} of Priestley spaces is a compactification of their disjoint union, and that this compactification in turn can be organized into a union of pairwise disjoint order independent closed subspaces Xu, indexed by the ultrafilters u on the index set I. The nature of those subspaces Xu indexed by the free ultrafilters u is not yet fully u...