COFINAL TYPES BELOW

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

ROY SHALEV

{"title":"COFINAL TYPES BELOW","authors":"ROY SHALEV","doi":"10.1017/jsl.2023.32","DOIUrl":null,"url":null,"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.","PeriodicalId":501300,"journal":{"name":"The Journal of Symbolic Logic","volume":"63 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Journal of Symbolic Logic","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/jsl.2023.32","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

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.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

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。

求助全文

约1分钟内获得全文去求助

来源期刊

The Journal of Symbolic Logic

自引率

0.00%

发文量

期刊最新文献

ARTIN–SCHREIER EXTENSIONS AND COMBINATORIAL COMPLEXITY IN HENSELIAN VALUED FIELDS ONE-DIMENSIONAL SUBGROUPS AND CONNECTED COMPONENTS IN NON-ABELIAN p-ADIC DEFINABLE GROUPS BUILDING MODELS IN SMALL CARDINALS IN LOCAL ABSTRACT ELEMENTARY CLASSES Generic Expansions of Geometric Theories Discontinuous Homomorphisms of with