Remarks on partitioner algebras

Abstract

Partitioner algebras are defined in [1] and are a natural tool for studying the properties of maximal almost disjoint families of subsets of ω \omega . We answer negatively two questions which were raised in [1]. We prove that there is a model in which the class of partitioner algebras is not closed under quotients and that it is consistent that there is a Boolean algebra of cardinality ℵ 1 {\aleph _1} which is not a partitioner algebra.