Thick sets and the Central Set Theorem

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2025-07-25 DOI:10.1016/j.apal.2025.103645

Teng Zhang

引用次数: 0

Abstract

In 1981, Furstenberg introduced the notion of central sets, and he established the Central Set Theorem. Since then, several generalizations of this result have been found, where a significant version is obtained by De, Hindman and Strauss. In this article, we find that the Central Set Theorem can be improved further. And we observe that there are some connections between thick sets and J-sets. Based on that, we establish a CST-type result for thick sets. Moreover, we introduce a new notion called super thick sets, and find that this notion has rich combinatorial properties. In particular, it contains additive and multiplicative structures, and it has a CST-type result for two operations. In addition, it can be partitioned into κ super thick subsets in very weakly cancellative weak rings with size κ.

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厚集与中心集定理

1981年，Furstenberg引入了中心集的概念，并建立了中心集定理。从那时起，对这一结果进行了几次推广，其中De， Hindman和Strauss得到了一个重要的版本。在本文中，我们发现中心集定理是可以进一步改进的。我们观察到在厚集和j集之间存在一些联系。在此基础上，我们建立了厚集的cst型结果。此外，我们引入了一个新的概念——超粗集，并发现这个概念具有丰富的组合性质。特别是，它包含加法和乘法结构，并且对于两个操作具有cst类型的结果。此外，它可以在大小为κ的非常弱消弱环中划分为κ超厚子集。

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

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.