On Schauder equivalence relations

Xin Ma

doi:10.1002/malq.201600074

On Schauder equivalence relations

Xin Ma^*

^*Corresponding author for this work

Texas A&M University

Research output: Contribution to journal › Article › peer-review

Abstract

We study Schauder equivalence relations, which are Borel equivalence relations induced by actions of Banach spaces with Schauder bases. Firstly, we show that R^ω/l₁ and R^ω/c₀ are minimal Schauder equivalence relations. Then, we prove that neither of them is Borel reducible to the quotient R^ω where T is the Tsirelson space. This implies that they cannot form a basis for the Schauder equivalence relations. In addition, we apply an argument of Farah to show that every basis for the Schauder equivalence relations, if such exist, has to be of cardinality 2^ℵ0.

Original language	English
Pages (from-to)	491-500
Number of pages	10
Journal	Mathematical Logic Quarterly
Volume	63
Issue number	6
DOIs	https://doi.org/10.1002/malq.201600074
State	Published - Dec 2017
Externally published	Yes

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title = "On Schauder equivalence relations",

abstract = "We study Schauder equivalence relations, which are Borel equivalence relations induced by actions of Banach spaces with Schauder bases. Firstly, we show that Rω/l1 and Rω/c0 are minimal Schauder equivalence relations. Then, we prove that neither of them is Borel reducible to the quotient Rω where T is the Tsirelson space. This implies that they cannot form a basis for the Schauder equivalence relations. In addition, we apply an argument of Farah to show that every basis for the Schauder equivalence relations, if such exist, has to be of cardinality 2ℵ0.",

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AB - We study Schauder equivalence relations, which are Borel equivalence relations induced by actions of Banach spaces with Schauder bases. Firstly, we show that Rω/l1 and Rω/c0 are minimal Schauder equivalence relations. Then, we prove that neither of them is Borel reducible to the quotient Rω where T is the Tsirelson space. This implies that they cannot form a basis for the Schauder equivalence relations. In addition, we apply an argument of Farah to show that every basis for the Schauder equivalence relations, if such exist, has to be of cardinality 2ℵ0.

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DO - 10.1002/malq.201600074

M3 - 文章

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SN - 0942-5616

VL - 63

SP - 491

EP - 500

JO - Mathematical Logic Quarterly

JF - Mathematical Logic Quarterly

IS - 6

ER -

On Schauder equivalence relations

Abstract

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