Skip to main content
SpringerLink
Log in

Borel equivalence relations between ℓ 1 and ℓ p

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this paper, we show that, for each p > 1, there are continuum many Borel equivalence relations between ℝωℓ1 and ℝωℓ p ordered by ≤B which are pairwise Borel incomparable.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Dougherty, R., Hjorth, G.: Reducibility and nonreducibility between ℓ p equivalence relations. Trans. Amer. Math. Soc., 351, 1835–1844 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  2. Gao, S.: Invariant Descriptive Set Theory, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 293, CRC Press, Boca Raton, 2008

    Google Scholar 

  3. Gao, S.: Equivalence Relations and Classical Banach Spaces. In: Mathematical Logic in Asia, World Sci. Publ., Hackensack, NJ, 2006, 70–89

    Chapter  Google Scholar 

  4. Kechiris, A. S.: Classical Descriptive Set Theory, Graduate Texts in Mathematics, Vol. 156, Springer-Verlag, New York, 1995

    Google Scholar 

  5. Mátrai, T.: On ℓ p-like equivalence relations. Real Anal. Exchange, 34(2), 377–412 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical Sciences and LPMC, Nankai University, Tianjin, 300071, P. R. China

    Long Yun Ding & Zhi Yin

Authors
  1. Long Yun Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Long Yun Ding.

Additional information

The first author is supported by National Natural Science Foundation of China (Grant No. 11071129) and Program for New Century Excellent Talents in University (Grant No. 09-0477)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ding, L.Y., Yin, Z. Borel equivalence relations between ℓ 1 and ℓ p . Acta. Math. Sin.-English Ser. 29, 2391–2396 (2013). https://doi.org/10.1007/s10114-013-2110-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-013-2110-7

Keywords

MR(2010) Subject Classification

Search

Navigation