$κ$-barely independent families and Tukey types of ultrafilters
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912497981718528 |
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| author | Chapital, Jorge Antonio Cruz |
| author_facet | Chapital, Jorge Antonio Cruz |
| contents | Given two infinite cardinals $κ$ and $λ$, we introduce and study the notion of a $κ$-barely independent family over $λ.$ We provide some conditions under which these types of families exist. In particular, we relate the existence of large $κ$-barely independent families with the generalized reaping numbers $\mathfrak{r}(κ,λ)$ and use these relations to give conditions under which every uniform ultrafilter over a given cardinal $λ$ is both Tukey top and has maximal character. Finally, we show that $\mathfrak{p}>ω_1$ the non-existence of barely independent families over $ω_1.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $κ$-barely independent families and Tukey types of ultrafilters Chapital, Jorge Antonio Cruz Logic 03E17, 03E10, 03E35, 03E05, 03E20 Given two infinite cardinals $κ$ and $λ$, we introduce and study the notion of a $κ$-barely independent family over $λ.$ We provide some conditions under which these types of families exist. In particular, we relate the existence of large $κ$-barely independent families with the generalized reaping numbers $\mathfrak{r}(κ,λ)$ and use these relations to give conditions under which every uniform ultrafilter over a given cardinal $λ$ is both Tukey top and has maximal character. Finally, we show that $\mathfrak{p}>ω_1$ the non-existence of barely independent families over $ω_1.$ |
| title | $κ$-barely independent families and Tukey types of ultrafilters |
| topic | Logic 03E17, 03E10, 03E35, 03E05, 03E20 |
| url | https://arxiv.org/abs/2507.17124 |