Square compactness and Lindelöf trees

IF 0.4 4区数学 Q4 LOGIC

Archive for Mathematical Logic Pub Date : 2024-04-10 DOI:10.1007/s00153-024-00918-5

Pedro E. Marun

引用次数: 0

Abstract

We prove that every weakly square compact cardinal is a strong limit cardinal, and therefore weakly compact. We also study Aronszajn trees with no uncountable finitely splitting subtrees, characterizing them in terms of being Lindelöf with respect to a particular topology. We prove that the class of such trees is consistently non-empty and lies between the classes of Suslin and Aronszajn trees.

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平方紧凑性和林德洛夫树

我们证明了每一个弱平方紧凑心形都是强极限心形，因此也是弱紧凑心形。我们还研究了没有不可数有限分裂子树的阿伦扎金树，并根据林德洛夫与特定拓扑学的关系来描述它们。我们证明，这类树始终是非空的，介于苏斯林树和阿伦扎任树之间。

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 数学-数学

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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.