Representing free Boolean algebras
Partitioner algebras are defined in  and are natural tools for studying the properties of maximal almost disjoint families of subsets of ω. In this paper we investigate which free algebras can be represented as partitioner algebras or as subalgebras of partitioner algebras. In so doing we answer a question raised in  by showing that the free algebra with $ℵ_1$ generators is represented. It was shown in  that it is consistent that the free Boolean algebra of size continuum is not a subalgebra of any partitioner algebra.