On the extendability to $\mathbf {\Pi }_3^0$ ideals and Katětov order

IF 0.3 4区数学 Q1 Arts and Humanities Archive for Mathematical Logic Pub Date : 2024-02-26 DOI:10.1007/s00153-024-00912-x

Jialiang He, Jintao Luo, Shuguo Zhang

引用次数: 0

Abstract

We show that there is a $ \varvec{\Sigma }_4^0$ ideal such that it’s neither extendable to any $ \varvec{\Pi }_3^0$ ideal nor above the ideal $ \textrm{Fin}\times \textrm{Fin} $ in the sense of Katětov order, answering a question from M. Hrušák.

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关于向 $$\mathbf {\Pi }_3^0$$ 理想和 Katětov 秩的可扩展性

我们证明了存在这样一个理想：它既不能扩展到任何理想，也不能高于卡泰托夫阶意义上的理想（\textrm{Fin}\times \textrm{Fin} \），这回答了赫鲁沙克（M. Hrušák）的一个问题。

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

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

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审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.

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On the extendability to \(\mathbf {\Pi }_3^0\) ideals and Katětov order

Abstract