A STRONG PROPERTY OF THE WEAK SUBALGEBRA LATTICE FOR LOCALLY FINITE ALGEBRAS OF FINITE TYPE

The aim of this paper is to show that the weak subalgebra lattice uniquely determines the subalgebra lattice for locally finite algebras of a fixed finite type. However, this algebraic result turns out to be a very particular case of the following hypergraph result (which is interesting itself): A total directed hypergraph D of finite type is uniquely determined, in the class of all the directed hypergraphs of this type, by its skeleton up to the orientation of some pairwise edge-disjoint directed hypercycles and hyperpaths. The skeleton of D is a hypergraph obtained from D by omitting the orientation of all edges.