  We recall some classical results relating normality and some natural
weakenings of normality in $\Psi$-spaces over almost disjoint families of
branches in the Cantor tree to special sets of reals like $Q$-sets,
$\lambda$-sets and $\sigma$-sets. We introduce a new class of special sets of
reals which corresponds the corresponding almost disjoint family of branches
being $\aleph_0$-separated. This new class fits between $\lambda$-sets and
perfectly meager sets. We also discuss conditions for an almost disjoint family
$\mathcal A$ being potentially almost-normal (pseudonormal), in the sense that
$\mathcal A$ is almost-normal (pseudonormal) in some c.c.c. forcing extension.
