无扭无边群是伯尔完全群 | 数学年鉴

IF 5.7 1区数学 Q1 MATHEMATICS

Annals of Mathematics Pub Date : 2024-05-01 DOI:10.4007/annals.2024.199.3.4

Gianluca Paolini, Saharon Shelah

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引用次数: 0

摘要

我们证明了具有域 $\omega$ 的无扭无边群的伯尔空间是伯尔完全的，即这个伯尔空间上的同构关系是尽可能复杂的同构关系。这就解决了描述集合论中一个长期悬而未决的问题，这个问题可以追溯到弗里德曼和斯坦利在 1989 年发表的关于 Borel 还原性的开创性论文。

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Torsion-free abelian groups are Borel complete | Annals of Mathematics

We prove that the Borel space of torsion-free abelian groups with domain $\omega$ is Borel complete, i.e., the isomorphism relation on this Borel space is as complicated as possible, as an isomorphism relation. This solves a long-standing open problem in descriptive set theory, which dates back to the seminal paper on Borel reducibility of Friedman and Stanley from 1989.

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来源期刊

Annals of Mathematics 数学-数学

CiteScore

9.10

自引率

2.00%

发文量

审稿时长

12 months

期刊介绍： The Annals of Mathematics is published bimonthly by the Department of Mathematics at Princeton University with the cooperation of the Institute for Advanced Study. Founded in 1884 by Ormond Stone of the University of Virginia, the journal was transferred in 1899 to Harvard University, and in 1911 to Princeton University. Since 1933, the Annals has been edited jointly by Princeton University and the Institute for Advanced Study.