Algebras that are hereditarily interval

Abstract

Interval algebras are a class of Boolean algebras with a linearly ordered set of generators. This class of algebras is not hereditary, i.e., not closed under taking subalgebras. We investigate the problem of finding a natural subclass of this class that is hereditary. For example, we prove that s-centered subalgebras of interval algebras of size less than b are interval algebras themselves. We state a dual form of our result saying that continuous zero-dimensional images of ordered compacta of weight less than b are themselves ordered.