Homogeneous and universal Dedekind algebras (Q1975161)

A Dedekind algebra is an ordered pair \((B,h)\) where \(B\) is a non-empty set and \(h\) is a similarity transformation on \(B\). Each Dedekind algebra is associated with a cardinal-valued function on \(\omega\) called its configuration signature (the configuration signature counts the number of configurations in each isomorphism type which occur in the decomposition of the algebra). The aim of this paper is to prove that configuration signatures can be used to characterize the homogeneous, universal and homogeneous-universal Dedekind algebras. This characterization is used to prove various results about these subclasses of Dedekind algebras.