Abstract

A Priestley duality is developed for the variety jω of all modal lattices. This is achieved by restricting to jω a known Priestley duality for the variety of all bounded distributive lattices with a meet-homomorphism. The variety jω was first studied by R. Beazer in 1986.The dual spaces of free modal lattices are constructed, paralleling P.R. Halmos' construction of the dual spaces of free monadic Boolean algebras and its generalization, by R. Cignoli, to distributive lattices with a quantifier.