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arXiv · 2308.12136

Game-theoretic variants of cardinal invariants

Jorge Antonio Cruz Chapital·Tatsuya Goto·Yusuke Hayashi
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Abstract

We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are 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.

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Jorge Antonio Cruz Chapital, Tatsuya Goto, Yusuke Hayashi. 2023-08-23. Game-theoretic variants of cardinal invariants. https://arxiv.org/abs/2308.12136

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