Duality for Bounded Lattices

Folks, there is a paper available via ftp to cs.indiana.edu in the
pub/logic directory called duality.ps (.dvi). The abstract follows below.
Lattices are in used in the algebraic semantics of linear logics. The duality
was extended to the full Kripke models in my thesis and a paper on that
should also appear shortly...real soon...really...


Duality for Bounded Lattices

Gerard T. Allwein                Chrysafis Hartonas
Visual Inference Laboratory      Dept of Math and Philosophy
Indiana University               Indiana University

We present a duality theorem for bounded lattices
that improves and strengthens Urquhart's topological
representation for lattices. Rather than using maximal, disjoint
filter-ideal pairs, as Urquhart does, we use all disjoint filter-ideal
pairs. This allows not only for establishing a bijective
correspondance between lattices and a certain kind of
doubly ordered Stone Spaces (Urquhart), but for a full
duality result. We provide, in the sequel, a treatment
of congruences and epimorphisms, as well as of sublattices,
proving relevant duality theorems. The paper is concluded with
a sectional representation of lattices, imbedding a general
lattice in a sheaf space of lattices.