Abstract

Heidorf, L., Moderate families in Boolean algebras, Annals of Pure and Applied Logic 57 217–250. A subset F of a Boolean algebra B will be called moderate if no element of B splits infinitely many elements of F . Disjoint moderate sets occur in connection with a product construction that is systematically studied in this paper. In contrast to the usual full direct product, these so-called moderate products preserve many properties of their factors. This can be used, for example, to construct big retractive Boolean algebras that are not embeddable into interval algebras. The paper is also concerned with those Boolean algebras whose ideals are generated by moderate sets. The results may be summarized by saying that in many respects these algebras behave like countable ones