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arXiv · 2507.17124

$κ$-barely independent families and Tukey types of ultrafilters

Jorge Antonio Cruz Chapital
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Abstract

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 $ω_1.$

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Jorge Antonio Cruz Chapital. 2025-07-23. $κ$-barely independent families and Tukey types of ultrafilters. https://arxiv.org/abs/2507.17124

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