Game-theoretic variants of cardinal invariants
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913592523096064 |
|---|---|
| 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 |