Maximal almost disjoint families of functions
We study maximal almost disjoint (MAD) families of functions in that satisfy certain strong combinatorial properties. In particular, we study the notions of strongly and very MAD families of functions. We introduce and study a hierarchy of combinatorial properties lying between strong MADness and very MADness. Proving a conjecture of Brendle, we show that if , then there no very MAD families. We answer a question of Kastermans by constructing a strongly MAD family from = . Next, we study the...