More on Configurations in Priestley Spaces, and Some New Problems

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...

FUZZY ORDERED SETS AND DUALITY FOR FINITE FUZZY DISTRIBUTIVE LATTICES

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

Configurations in Coproducts of Priestley Spaces

Configurations in Coproducts of Priestley Spaces

Let P be a configuration, i.e., a finite poset with top element. Let Forb(P ) be the class of bounded distributive lattices L whose Priestley space P(L) contains no copy of P . We show that the following are equivalent: Forb(P ) is first-order definable, i.e., there is a set of first-order sentences in the language of bounded lattice theory whose satisfaction characterizes membership in Forb(P ...

Dualities in Lattice Theory

In this note we prove several duality theorems in lattice theory. We also discuss the connection between spectral spaces and Priestley spaces, and interpret Priestley duality in terms of spectral spaces. The organization of this note is as follows. In the first section we collect appropriate definitions and basic results common to many of the various topics. The next four sections consider Birk...