Priestley spaces

Stone Spaces versus Priestley Spaces

[1] B. Banaschewski, Über nulldimensionale Räume, Math. Nache 13 (1955) 129-140. [2] F. Borceux and J. Janelidze, Galois Theories, Cambridge University Press (2001). [3] M. Dias and M. Sobral, Descent for Priestley Spaces, Appl. Categor. Struct 14 (2006) 229-241. [4] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge Mathematical Texbooks (1990). [5] R. Engelking and...

Descent for Priestley Spaces

A characterization of descent morphism in the category of Priestley spaces, as well as necessary and sufficient conditions for such morphisms to be effective are given. For that we embed this category in suitable categories of preordered topological spaces were descent and effective morphisms are described using the monadic description of descent.

Forbidden Forests in Priestley Spaces

We present a first order formula characterizing the distributive lattices L whose Priestley spaces P(L) contain no copy of a finite forest T . For Heyting algebras L, prohibiting a finite poset T in P(L) is characterized by equations iff T is a tree. We also give a condition characterizing the distributive lattices whose Priestley spaces contain no copy of a finite forest with a single addition...

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 ...