The Almost Disjointness Cardinal Invariant in the Quotient Algebra of the Rationals Modulo the Nowhere Dense Subsets

Abstract

The almost disjointness number is extended to arbitrary Boolean algebras and it is shown that this number is consistently less than $\mathfrak a$ for the Boolean algebra $\mathcal {P} (\mathbb{N})/ \mathcal {N}$ where $\mathcal {N}$ is the ideal of nowhere dense subsets of $\mathbb{Q}.