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EMBEDDINGS OF P(ω)/Fin INTO BOREL EQUIVALENCE RELATIONS BETWEEN ℓp AND ℓq

Published online by Cambridge University Press:  22 July 2015

ZHI YIN
ZHI YIN*
Affiliation:
SCHOOL OF MATHEMATICS NANKAI UNIVERSITY TIANJIN, 300071 P.R.CHINAE-mail: will.yin@hotmail.com
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Abstract

We prove that, for 1 ≤ p < q < ∞, the partially ordered set P(ω)/Fin can be embedded into Borel equivalence relations between ℝω/ℓp and ℝω/ℓq. Since there is an antichain of size continuum in P(ω)/Fin, there are continuum many pairwise incomparable Borel equivalence relations between ℝω/ℓp and ℝω/ℓq.

Keywords

Primary 03E15Secondary 46B45Equivalence relationBorel reducibilityℓpP(ω)/Fin
Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 3 , September 2015 , pp. 917 - 939
Copyright
Copyright © The Association for Symbolic Logic 2015 

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