小红雀的全苏树林

IF 1 2区数学 Q1 MATHEMATICS Journal of the London Mathematical Society-Second Series Pub Date : 2024-06-28 DOI:10.1112/jlms.12957

Assaf Rinot, Shira Yadai, Zhixing You

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引用次数: 0

摘要

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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Full Souslin trees at small cardinals

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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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.