Journal of Symbolic Logic 77 (1):224-244 (2012)

Abstract
We investigate Borel reducibility between equivalence relations $E(X;p)=X^{\mathbb{N}}/\ell_{p}(X)'s$ where X is a separable Banach space. We show that this reducibility is related to the so called Hölder(α) embeddability between Banach spaces. By using the notions of type and cotype of Banach spaces, we present many results on reducibility and unreducibility between E(L r ; p)'s and E(c 0 ; p)'s for r, p ∈ [1, +∞). We also answer a problem presented by Kanovei in the affirmative by showing that $\mathrm{C}\left({\mathrm{\mathbb{R}}}^{+}\right)/{\mathrm{C}}_{0}\left({\mathrm{\mathbb{R}}}^{+}\right)$ is Borel bireducible to $\mathbb{R}^{\mathbb{N}}/c_{0}$
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DOI 10.2178/jsl/1327068700
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References found in this work BETA

Actions by the Classical Banach Spaces.G. Hjorth - 2000 - Journal of Symbolic Logic 65 (1):392-420.

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Citations of this work BETA

Borel Reducibility and Finitely Hölder (Α) Embeddability.Longyun Ding - 2011 - Annals of Pure and Applied Logic 162 (12):970-980.
A Note on Equivalence Relations ℓp.Su Gao & Zhi Yin - 2015 - Mathematical Logic Quarterly 61 (6):516-523.
Characterization of ℓp-Like and C0 -Like Equivalence Relations.Longyun Ding - 2014 - Mathematical Logic Quarterly 60 (4-5):273-279.
On Schauder Equivalence Relations.Xin Ma - 2017 - Mathematical Logic Quarterly 63 (6):491-500.

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