• 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}
}
. 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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