Notre Dame Journal of Formal Logic

Canonization of Smooth Equivalence Relations on Infinite-Dimensional E0-Large Products

Vladimir Kanovei and Vassily Lyubetsky

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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(ℓ)=y(ℓ), and x↾(ω∖{ℓ})=y↾(ω∖{ℓ}) implies xFy.

Article information

Source
Notre Dame J. Formal Logic, Volume 61, Number 1 (2020), 117-128.

Dates
Received: 28 April 2018
Accepted: 26 November 2018
First available in Project Euclid: 12 December 2019

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1576120172

Digital Object Identifier
doi:10.1215/00294527-2019-0034

Subjects
Primary: 03E15: Descriptive set theory [See also 28A05, 54H05]
Secondary: 03E35: Consistency and independence results

Keywords
canonization smooth equivalences infinite products $E_{0}$-large

Citation

Kanovei, Vladimir; Lyubetsky, Vassily. Canonization of Smooth Equivalence Relations on Infinite-Dimensional $\mathsf{E}_{0}$ -Large Products. Notre Dame J. Formal Logic 61 (2020), no. 1, 117--128. doi:10.1215/00294527-2019-0034. https://projecteuclid.org/euclid.ndjfl/1576120172


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References

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Notre Dame Journal of Formal Logic

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