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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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References

REFERENCES

Baumgartner, J., Frankiewicz, R., and Zbierski, P., Embeddings of Boolean algebras in P(ω)/fin. Fundamenta Mathematicae, vol. 136 (1990), pp. 187–192.CrossRefGoogle Scholar
Bella, A., Dow, A., Hart, K. P., Hrusak, M., van Mill, J., and Ursino, P., Embeddings into P(ℕ)/fin and extension of automorphisms. Fundamenta Mathematicae, vol. 174 (2002), no. 3, pp. 271–284.CrossRefGoogle Scholar
Ding, L., Borel reducibility and finitely Hölder(α) embeddability. Annals of Pure and Applied Logic, vol. 162 (2011), pp. 970–980.CrossRefGoogle Scholar
Ding, L., A trichotomy for a class of equivalence relations. Science China Mathematics, vol. 55 (2012), no. 12, pp. 2621–2630.CrossRefGoogle Scholar
Ding, L., Borel reducibility and Hölder(α) embeddability between Banach spaces, this Journal, vol. 77 (2012), no. 1, pp. 224–244.Google Scholar
Ding, L. and Yin, Z., Borel equivalence relations between ℓ 1and ℓp. Acta Mathematica Sinica, English Series, vol. 29 (2013), no. 12, pp. 2391–2396.CrossRefGoogle Scholar
Dougherty, R. and Hjorth, G., Reducibility and nonreducibility between ℓp equivalence relations.Transcations of the American Mathematical Society, vol. 351 (1999), no. 5, pp. 1835–1844.CrossRefGoogle Scholar
Farah, I., Basic problem for turbulent actions II: c 0-equalities. Proceedings of the London Mathematical Society, vol. 82 (2001), no. 3, pp. 1–30.CrossRefGoogle Scholar
Gao, S., Equivalence relations and classical Banach spaces, Mathematical Logic in Asia, World Science Publisher, Hackensack, NJ, 2006, pp. 70–89.CrossRefGoogle Scholar
Gao, S., Invariant descriptive set theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 293, CRC Press, New York, 2008.CrossRefGoogle Scholar
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I: Sequence Spaces, Springer-Verlag, Berlin, 1977.CrossRefGoogle Scholar
Louveau, A. and Velickovic, B., A note on Borel equivalence relations. Proceedings of the American Mathemtaical Society, vol. 120 (1994), no. 1, pp. 255–259.CrossRefGoogle Scholar
Mátrai, T., On ℓp-like equivalence relations. Real Analysis Exchange, vol. 34 (2008), no. 2, pp. 377–412.CrossRefGoogle Scholar
Rosendal, C., Cofinal families of Borel equivalence relations and quasiorders, this Journal, vol. 70 (2005), no. 4, pp. 1325–1340.Google Scholar