COFINAL TYPES BELOW

The Journal of Symbolic Logic Pub Date : 2023-07-24 DOI:10.1017/jsl.2023.32

ROY SHALEV

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引用次数: 1

Abstract

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 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.

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Cofinal类型如下

证明了对于每一个正整数n，基数$\leq \aleph _n$的非tukey等价有向集的个数至少为$c_{n+2}$，即$(n+2)$ -加泰罗尼亚数。此外，基数$\leq \aleph _n$的有向集的$\mathcal D_{\aleph _n}$类包含Dyck $(n+2)$ -paths的偏置集的同构副本。此外，我们给出了副本中两个连续元素之间是否包含另一个有向集的完整描述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

The Journal of Symbolic Logic

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0.00%

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