Game-theoretic variants of cardinal invariants

Jorge Antonio Cruz Chapital, Tatsuya Goto, Yusuke Hayashi

Published 2023-08-23Version 1

We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the splitting number $\mathfrak{s}$, the reaping number $\mathfrak{r}$, the bounding number $\mathfrak{b}$, the dominating number $\mathfrak{d}$ and the additivity number of the null ideal $\operatorname{add}(\mathsf{null})$. We also consider games, called tallness games, defined according to ideals on $\omega$ and characterize that each of Player I and Player II has a winning strategy.