Every CBER is smooth below the Carlson–Simpson generic partition

IF 0.5 3区 数学 Q3 MATHEMATICS
Aristotelis Panagiotopoulos, Allison Wang
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引用次数: 0

Abstract

Let $E$ be a countable Borel equivalence relation on the space $\mathcal{E}_{\infty}$ of all infinite partitions of the natural numbers. We show that $E$ coincides with equality below a Carlson-Simpson generic element of $\mathcal{E}_{\infty}$. In contrast, we show that there is a hypersmooth equivalence relation on $\mathcal{E}_{\infty}$ which is Borel bireducible with $E_1$ on every Carlson-Simpson cube. Our arguments are classical and require no background in forcing.
在Carlson–Simpson泛型分区下,每个CBER都是光滑的
设$E$是空间$\mathcal上的可数Borel等价关系{E}_{\infty}$的所有自然数的无限分区。我们证明了$E$在$\mathcal的Carlson Simpson泛型元素下与等式一致{E}_{infty}$。相反,我们证明了$\mathcal上存在一个超光滑等价关系{E}_{\infty}$,它与每个Carlson Simpson立方体上的$E_1$是Borel可双导的。我们的论点是经典的,不需要强迫的背景。
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
Fundamenta Mathematicae
Fundamenta Mathematicae 数学-数学
CiteScore
1.00
自引率
0.00%
发文量
44
审稿时长
6-12 weeks
期刊介绍: FUNDAMENTA MATHEMATICAE concentrates on papers devoted to Set Theory, Mathematical Logic and Foundations of Mathematics, Topology and its Interactions with Algebra, Dynamical Systems.
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