• Corpus ID: 250113695

# Every CBER is smooth below the Carlson-Simpson generic partition

```@inproceedings{Panagiotopoulos2022EveryCI,
title={Every CBER is smooth below the Carlson-Simpson generic partition},
author={Aristotelis Panagiotopoulos and Allison Wang},
year={2022}
}```
• Published 28 June 2022
• Mathematics
. Let E be a countable Borel equivalence relation on the space E ∞ of all inﬁnite partitions of the natural numbers. We show that E coincides with equality below a Carlson-Simpson generic element of E ∞ . In contrast, we show that there is a hypersmooth equivalence relation on E ∞ 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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