Mad families of vector subspaces and the smallest nonmeager set of reals

Abstract

We show that a parametrized $♢$ principle, corresponding to the uniformity of the meager ideal, implies that the minimum cardinality of an infinite maximal almost disjoint family of block subspaces in a countable vector space is ${\aleph }_1$. Consequently, this cardinal invariant is ${\aleph }_1$ in the Miller model.

8 pages