Mad families of vector subspaces and the smallest nonmeager set of reals
Volume 163 / 2021
Colloquium Mathematicum 163 (2021), 15-22
MSC: Primary 03E17; Secondary 15A03.
DOI: 10.4064/cm8044-12-2019
Published online: 20 May 2020
Abstract
We show that a parametrized $\diamondsuit $ 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. This verifies a conjecture of the author from his previous article Madness in vector spaces (J. Symbolic Logic, 2019).
