STRUCTURE OF SUMMABLE TALL IDEALS UNDER KATĚTOV ORDER

被引：0

作者：

He, Jialiang ^{[1
]}

Li, Zuoheng ^{[1
]}

Zhang, Shuguo ^{[1
]}

机构：

[1] Sichuan Univ, Coll Math, 24, South Sect, Yihuan Rd, Chengdu, Sichuan 610065, Peoples R China

来源：

JOURNAL OF SYMBOLIC LOGIC | 2023年

关键词：

summable ideal; Katetov order; Galois-Tukey connection;

D O I：

10.1017/jsl.2023.24

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that Katetov and Rudin-Blass orders on summable tall ideals coincide. We prove that Katetov order on summable tall ideals is Galois-Tukey equivalent to $(\omega <^>\omega ,\le <^>*)$. It follows that Katetov order on summable tall ideals is upwards directed which answers a question of Minami and Sakai. In addition, we prove that ${l_\infty }$ is Borel bireducible to an equivalence relation induced by Katetov order on summable tall ideals.

引用

页数：27

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