MAD families of projections on l ² and real-valued functions on ω

Abstract

Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [ω]^ω and ω ^ω have been studied for quite some time. In particular, the cardinal invariants ${\mathfrak{a}}$ and ${\mathfrak{a}_e}$, defined to be the minimum cardinality of a maximal infinite almost disjoint family of [ω]^ω and ω ^ω respectively, are known to be consistently less than ${\mathfrak{c}}$. Here we examine analogs for functions in ${\mathbb{R}^\omega}$ and projections on l ², showing that they too can be consistently less than ${\mathfrak{c}}$.