1. Introduction Stone, in [8], developed for distributive lattices a representation theory generalizing that for Boolean algebras. This he achieved by topologizing the set X of prime ideals of a distributive lattice A (with a zero element) by taking as a base {P a : aeA} (where P a denotes the set of prime ideals of A not containing a), and by showing that the map a i-> P a is an isomorphism re...

Disjunctive systems are a representation of L-domains. They use sequents of the form X ` Y , with X nite and Y pairwise disjoint. We show that for any disjunctive system, its elements ordered by inclusion form an L-domain. On the other hand, via the notion of stable neighborhoods, every L-domain can be represented as a disjunctive system. More generally, we have a categorical equivalence betwee...

A locally modular (resp. locally distributive) lattice is a lattice with a congruence relation and each of whose equivalence class has sufficiently many elements and is a modular (resp. distributive) sublattice. Both the lattice of all closed subspaces of a locally convex space and the lattice of projections of a locally finite von Neumann algebra are locally modular. The lattice of all /^-topo...

It is shown that a finite lattice L is isomorphic to the interval between two Hausdorff topologies on some set if and only if L is distributive. The corresponding results had previously been shown in ZFC for intervals between T1 topologies and, assuming the existence of infinitely many measurable cardinals, for intervals between T3 topologies. Mathematics Subject Classifications (1991): Primary...

This paper presents an equivalence result between computability in the BSS model and in a suitable distributive category. It is proved that the class of functions R m ! R n (with n;m nite and R a commutative, ordered ring) computable in the BSS model, and the functions distributively computable over a natural distributive graph based on the operations of R coincide. Using this result, a new str...

Distributive supermatroids generalize matroids to partially ordered sets. Completing earlier work of Barnabei, Nicoletti and Pezzoli we characterize the lattice of flats of a distributive supermatroid. For the prominent special case of a polymatroid the description of the flat lattice is particularly simple. Large portions of the proofs reduce to properties of weakly submodular rank functions. ...

A complemented modular lattice L is coordinatizable, if it is isomorphic to the lattice L(R) of principal right ideals of some von Neumann regular ring R. All known sufficient conditions for coordinatizability, due first to J. von Neumann, then to B. Jónsson, are first-order. Nevertheless, we prove that coordinatizability of complemented modular lattices is not firstorder, even for countable 2-...

A complete lattice L is constructively completely distributive CCD L if the sup map de ned on down closed subobjects has a left adjoint It was known that in boolean toposes CCD L is equivalent to CCD L We show here that the latter property for all L su ciently for characterizes boolean toposes Research partially supported by grants from NSERC Canada Diagrams typeset using catmac Introduction Th...

In this paper, we have focused to study convex L-subgroups of an Lordered group. First, we introduce the concept of a convex L-subgroup and a convex L-lattice subgroup of an L-ordered group and give some examples. Then we find some properties and use them to construct convex L-subgroup generated by a subset S of an L-ordered group G . Also, we generalize a well known result about the set of all...

The complexity of a lattice polynomial is defined inductively, with variables having complexity 0. If p=plv'"vOk or p=plA'''/XOk is the canonical expression of the polynomial O, then the complexity c(p) = l+max{c(p~):l<-i-k}. An n-k lattice inclusion is an inclusion of the form p <-o-with c(p)<-n and c(o-)-k. In this note we use the main result of Day [1] to show that if all the congruence latt...