Cardinal functions on initial chain algebras on pseudotrees
A pseudotree is a partially ordered set such that the collection of elements below a given element is simply ordered. Taking those collections as generators, one forms a Boolean algebra of subsets of the pseudotree, called the initial chain algebra of it. The author investigates the relationships between the following common cardinal functions in such algebras: depth, tightness, spread, hereditary Lindelöf degree, cellularity, incomparability, hereditary cofinality, cardinality, and irredundance. Several theorems show that some of these functions coincide for initial chain algebras. The results seem to be rather complete. The Stone space of such an algebra is characterized.
scientific article; zbMATH DE number 1523422