Hereditary interval algebras and cardinal characteristics of the continuum

Abstract

An interval algebra is a Boolean algebra which is isomorphic to the algebra of finite unions of half-open intervals, of a linearly ordered set. An interval algebra is hereditary if every subalgebra is an interval algebra. We answer a question of M. Bekkali and S. Todorcevic, by showing that it is consistent that every σ-centered interval algebra of size $$\mathfrak{b}$$ is hereditary. We also show that there is, in ZFC, a hereditary interval algebra of cardinality ℵ1.