## Journal of Symbolic Logic

### Borel reducibility and Hölder(α) embeddability between Banach spaces

Longyun Ding

#### Abstract

We investigate Borel reducibility between equivalence relations E(X;p)=X/ℓp(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(Lr;p)'s and E(c₀;p)'s for r,p∈[1,+∞).

We also answer a problem presented by Kanovei in the affirmative by showing that C(ℝ⁺)/C₀(ℝ⁺) is Borel bireducible to ℝ/c₀.

#### Article information

Source
J. Symbolic Logic, Volume 77, Issue 1 (2012), 224-244.

Dates
First available in Project Euclid: 20 January 2012

https://projecteuclid.org/euclid.jsl/1327068700

Digital Object Identifier
doi:10.2178/jsl/1327068700

Mathematical Reviews number (MathSciNet)
MR2951638

Zentralblatt MATH identifier
1250.03082

Subjects
Primary: Primary 03E15, 46B20, 47H99

#### Citation

Ding, Longyun. Borel reducibility and Hölder(α) embeddability between Banach spaces. J. Symbolic Logic 77 (2012), no. 1, 224--244. doi:10.2178/jsl/1327068700. https://projecteuclid.org/euclid.jsl/1327068700

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