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arXiv · 0705.4297

Splitting families and the Noetherian type of $βω-ω$

David Milovich
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Abstract

Extending some results of Malykhin, we prove several independence results about base properties of $βω-ω$ and its powers, especially the Noetherian type $Nt(βω-ω)$, the least $κ$ for which $βω-ω$ has a base that is $κ$-like with respect to containment. For example, $Nt(βω-ω)$ is never less than the splitting number, but can consistently be that $ω_1$, $2^ω$, $(2^ω)^+$, or strictly between $ω_1$ and $2^ω$. $Nt(βω-ω)$ is also consistently less than the additivity of the meager ideal. $Nt(βω-ω)$ is closely related to the existence of special kinds of splitting families.

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David Milovich. 2008-03-27. Splitting families and the Noetherian type of $βω-ω$. https://arxiv.org/abs/0705.4297

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