Initial Chain Algebras on Pseudotrees

Abstract

We investigate a new class of Boolean algebra, called initial chain algebras on pseudotrees. We discuss the relationship between this class and other classes of Boolean algebras. Every interval algebra, and hence every countable Boolean algebra, is an initial chain algebra. Every initial chain algebra on a tree is a superatomic Boolean algebra, and every initial chain algebra on a pseudotree is a minimally-generated Boolean algebra. We show that a free product of two infinite Boolean algebras is an initial chain algebra if and only if both factors are countable.