Full Souslin trees at small cardinals

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY Accounts of Chemical Research Pub Date : 2024-06-28 DOI:10.1112/jlms.12957

Assaf Rinot, Shira Yadai, Zhixing You

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Abstract

A $κ$ -tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $κ$ -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal $κ$ . Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be $ℵ_{3}$ many full $ℵ_{2}$ -trees such that the product of any countably many of them is an $ℵ_{2}$ -Souslin tree.

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小红雀的全苏树林

如果κ $kappa$ -树的每个极限层都没有遗漏一个以上的潜在分支，那么这棵树就是完整的。库能（Kunen）问，一棵完整的κ $kappa$ -Souslin 树是否可能一直存在。谢拉给出了一个肯定的答案，即高度强极限马赫洛红心κ $\kappa $ 。这里，我们证明了这些树在小红心时可能一直存在。事实上，可以有ℵ 3 $\aleph _3$很多棵完整的ℵ 2 $\aleph _2$-树，使得其中任意可数棵树的乘积都是一棵ℵ 2 $\aleph _2$-苏林树。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.

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