Games on Base Matrices

Abstract

We show that base matrices for $\mathcal{P}(\mathit{\omega })∕\text{fin}$ of regular height larger than $\mathfrak{h}$ necessarily have maximal branches that are not cofinal. The same holds for base matrices of height $\mathfrak{h}$ if ${\mathfrak{t}}_{\mathrm{Spoiler}}<\mathfrak{h}$, where ${\mathfrak{t}}_{\mathrm{Spoiler}}$ is a variant of $\mathfrak{t}$ that has been introduced in “Construction with opposition: cardinal invariants and games” by Brendle, Hrušák, and Torres-Pérez.