Priestley configurations and Heyting varieties. (English) Zbl 1165.06003

Ball, Richard N.; Pultr, Aleš; Sichler, Jiří

Algebra Univers. 59, No. 1-2, 31-47 (2008).

The first two authors showed [Cah. Topol. Géom. Différ. Catég. 45, No. 1, 2–22 (2004; Zbl 1062.06020)] that the class of all Heyting algebras whose Priestley dual contains no copy of a given configuration forms a variety iff the configuration is a tree. The present paper characterizes finitely generated varieties of Heyting algebras given by prohibiting a system of trees in their Priestley duals.

Reviewer: Jiří Rosický (Brno)

MSC:

06D20	Heyting algebras (lattice-theoretic aspects)
06B20	Varieties of lattices
06D50	Lattices and duality
54F05	Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces

Keywords:

distributive lattice; Priestley duality; Heyting algebra; variety

Citations:

Zbl 1062.06020