在Carlson–Simpson泛型分区下，每个CBER都是光滑的

Pub Date : 2022-06-28 DOI:10.4064/fm255-12-2022

Aristotelis Panagiotopoulos, Allison Wang

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引用次数: 0

摘要

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。

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Every CBER is smooth below the Carlson–Simpson generic partition

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.

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