论文标题
高于$ \aleph_Ω$的高原类型
Cofinal types below $\aleph_ω$
论文作者
论文摘要
事实证明，对于每个正整数$ n $，非tukey等效的基数$ \ leq \ leq \ aleph_n $的数量至少为$ c_ {n+2} $，$（n+2）$ - catalan编号。此外，Tukey类$ \ MATHCAL D _ {\ ALEPH_N} $ of DIRECTED基数的基数$ \ leq \ Aleph_n $包含dyck $（n+2）$路径的Poset的同构副本。此外，我们提供了一个完整的描述，该副本中的两个连续元素是否包含另一个在之间的定向设置。
It is proved that for every positive integer $n$, the number of non-Tukey-equivalent directed sets of cardinality $\leq \aleph_n$ is at least $c_{n+2}$, the $(n+2)$-Catalan number. Moreover, the Tukey class $\mathcal D_{\aleph_n} $ of directed sets of cardinality $\leq \aleph_n$ contains an isomorphic copy of the poset of Dyck $(n+2)$-paths. Furthermore, we give a complete description whether two successive elements in the copy contain another directed set in between or not.
