论文标题
每个CBER都在卡尔森 - 辛普森通用分区下方平滑
Every CBER is smooth below the Carlson-Simpson generic partition
论文作者
论文摘要
令$ e $为空格$ \ Mathcal {e} _ {\ infty} $的空间上的可数鲍尔等效关系。我们表明，$ e $与$ \ mathcal {e} _ {\ infty} $的Carlson-simpson通用元素低于Carlson-Simpson的均等。相反，我们表明$ \ Mathcal {e} _ {\ infty} $上有一个高度平滑的对等关系，在每个Carlson-Simpson Cube上都是$ e_1 $。我们的论点是经典的，不需要强迫背景。
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.
