Canonization of Smooth Equivalence Relations on Infinite-Dimensional $mathsf{E}_{0}$-Large Products

Notre Dame Journal of Formal Logic 61 (1):117-128 (2020)

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Abstract
We propose a canonization scheme for smooth equivalence relations on Rω modulo restriction to E0-large infinite products. It shows that, given a pair of Borel smooth equivalence relations E, F on Rω, there is an infinite E0-large perfect product P⊆Rω such that either F⊆E on P, or, for some ℓ<ω, the following is true for all x,y∈P: xEy implies x=y, and x↾=y↾ implies xFy.
Keywords $E_{0}$-large   infinite products   smooth equivalences  canonization
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DOI 10.1215/00294527-2019-0034
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