Uniform refinement properties in distributive semilattices
by
Miroslav Ploščica
Mathematical Institute, Slovak Academy of Sciences, Kosice, Slovakia

There is a well-known problem in the lattice theory called the Congruence Lattice Problem (CLP): Is every distributive algebraic lattice isomorphic to congruence lattice of some lattice? There are some partial positive and negative results. The negative results are connected with various uniform refinement properties, first discovered by F. Wehrung about ten years ago. These properties are based on infinite combinatorics, especially the Kuratowski principle about free sets. So far, none of these properties could solve the CLP in full. Now we introduce a new uniform refinement property, weaker then the previous ones, and investigate its potential for soving the CLP and related problems.

Date received: May 21, 2004