分裂族与$βω-ω$的Noether型
Splitting families and the Noetherian type of $βω-ω$
摘要：
推广了Malykhin的一些结果，证明了$βω-ω$的基性质及其幂的几个独立性结果，特别是Noether型$Nt(βω-ω)$，即$βω-ω$的基在包容性方面是$κ$ -like的最小$κ$.例如，$Nt(βω-ω)$永远不会小于拆分数，但可以始终是$ω_1$、$2^ω$、$(2^ω)^+$，或者严格地介于$ω_1$和$2^ω$之间。$Nt(βω-ω)$也始终小于贫乏理想的可加性。$Nt(βω-ω)$与特殊类型分裂家庭的存在密切相关。
英文摘要：
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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