Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-26T18:26:26.984Z Has data issue: false hasContentIssue false

EMBEDDINGS OF P(ω)/Fin INTO BOREL EQUIVALENCE RELATIONS BETWEEN p AND q

Published online by Cambridge University Press:  22 July 2015

ZHI YIN*
Affiliation:
SCHOOL OF MATHEMATICS NANKAI UNIVERSITY TIANJIN, 300071 P.R.CHINAE-mail: [email protected]

Abstract

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

Type
Articles
Copyright
Copyright © The Association for Symbolic Logic 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Baumgartner, J., Frankiewicz, R., and Zbierski, P., Embeddings of Boolean algebras in P(ω)/fin. Fundamenta Mathematicae, vol. 136 (1990), pp. 187192.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. 271284.CrossRefGoogle Scholar
Ding, L., Borel reducibility and finitely Hölder(α) embeddability. Annals of Pure and Applied Logic, vol. 162 (2011), pp. 970980.CrossRefGoogle Scholar
Ding, L., A trichotomy for a class of equivalence relations. Science China Mathematics, vol. 55 (2012), no. 12, pp. 26212630.CrossRefGoogle Scholar
Ding, L., Borel reducibility and Hölder(α) embeddability between Banach spaces, this Journal, vol. 77 (2012), no. 1, pp. 224244.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. 23912396.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. 18351844.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. 130.CrossRefGoogle Scholar
Gao, S., Equivalence relations and classical Banach spaces, Mathematical Logic in Asia, World Science Publisher, Hackensack, NJ, 2006, pp. 7089.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. 255259.CrossRefGoogle Scholar
Mátrai, T., On p-like equivalence relations. Real Analysis Exchange, vol. 34 (2008), no. 2, pp. 377412.CrossRefGoogle Scholar
Rosendal, C., Cofinal families of Borel equivalence relations and quasiorders, this Journal, vol. 70 (2005), no. 4, pp. 13251340.Google Scholar