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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2308.12136 |
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| _version_ | 1866913592523096064 |
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| author | Chapital, Jorge Antonio Cruz Goto, Tatsuya Hayashi, Yusuke |
| author_facet | Chapital, Jorge Antonio Cruz Goto, Tatsuya Hayashi, Yusuke |
| contents | 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 $ω$ and characterize that each of Player I and Player II has a winning strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_12136 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Game-theoretic variants of cardinal invariants Chapital, Jorge Antonio Cruz Goto, Tatsuya Hayashi, Yusuke Logic 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 $ω$ and characterize that each of Player I and Player II has a winning strategy. |
| title | Game-theoretic variants of cardinal invariants |
| topic | Logic |
| url | https://arxiv.org/abs/2308.12136 |