Homogeneous and Universal Dedekind Algebras
Author: Weaver, G.
Source: Studia Logica, Volume 64, Number 2, February 2000 , pp. 173-192(20)
Abstract:A Dedekind algebra is an order pair (B, h) where B is a non-empty set and h is a similarity transformation on B. Each Dedekind algebra can be decomposed into a family of disjoint, countable subalgebras called the configurations of the algebra. There are ℵ_0 isomorphism types of configurations. Each Dedekind algebra is associated with a cardinal-valued function on called its configuration signature. The configuration signature counts the number of configurations in each isomorphism type which occur in the decomposition of the algebra. Two Dedekind algebras are isomorphic iff their configuration signatures are identical. It is shown 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.
Document Type: Regular Paper
Publication date: February 1, 2000