RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 1, Pages 59–82 (Mi izv418)  

This article is cited in 7 scientific papers (total in 7 papers)

Some new results on Borel irreducibility of equivalence relations

V. G. Kanovei, M. Reeken


Abstract: We prove that orbit equivalence relations (ERs, for brevity) of generically turbulent Polish actions are not Borel reducible to ERs of a family which includes Polish actions of $S_\infty$ (the group of all permutations of $\mathbb N$ and is closed under the Fubini product modulo the ideal Fin of all finite sets and under some other operations. We show that $\mathsf T_2$ (an equivalence relation called the equality of countable sets of reals is not Borel reducible to another family of ERs which includes continuous actions of Polish CLI groups, Borel equivalence relations with $\mathbf G_{\delta\sigma}$ classes and some ideals, and is closed under the Fubini product modulo Fin. These results and their corollaries extend some earlier irreducibility theorems of Hjorth and Kechris.

DOI: https://doi.org/10.4213/im418

Full text: PDF file (2692 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2003, 67:1, 55–76

Bibliographic databases:

UDC: 510.225
MSC: 03E15, 54E50
Received: 30.07.2001

Citation: V. G. Kanovei, M. Reeken, “Some new results on Borel irreducibility of equivalence relations”, Izv. RAN. Ser. Mat., 67:1 (2003), 59–82; Izv. Math., 67:1 (2003), 55–76

Citation in format AMSBIB
\Bibitem{KanRee03}
\by V.~G.~Kanovei, M.~Reeken
\paper Some new results on Borel irreducibility of equivalence relations
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 1
\pages 59--82
\mathnet{http://mi.mathnet.ru/izv418}
\crossref{https://doi.org/10.4213/im418}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1957916}
\zmath{https://zbmath.org/?q=an:1068.03036}
\transl
\jour Izv. Math.
\yr 2003
\vol 67
\issue 1
\pages 55--76
\crossref{https://doi.org/10.1070/IM2003v067n01ABEH000418}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000185513200004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33748479303}


Linking options:
  • http://mi.mathnet.ru/eng/izv418
  • https://doi.org/10.4213/im418
  • http://mi.mathnet.ru/eng/izv/v67/i1/p59

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Rosendal C., “Cofinal families of Borel equivalence relations and quasiorders”, J. Symbolic Logic, 70:4 (2005), 1325–1340  crossref  mathscinet  zmath  isi  scopus
    2. V. G. Kanovei, V. A. Lyubetskii, “A Cofinal Family of Equivalence Relations and Borel Ideals Generating Them”, Proc. Steklov Inst. Math., 252 (2006), 85–103  mathnet  crossref  mathscinet
    3. V. G. Kanovei, V. A. Lyubetskii, “Borel reducibility as an additive property of domains”, J. Math. Sci. (N. Y.), 158:5 (2009), 708–712  mathnet  crossref  elib  elib
    4. Thomas S., “On the complexity of the quasi-isometry and virtual isomorphism problems for finitely generated groups”, Groups Geom. Dyn., 2:2 (2008), 281–307  crossref  mathscinet  zmath  isi
    5. Thomas S., “A remark on the Higman–Neumann-Neumann embedding theorem”, J. Group Theory, 12:4 (2009), 561–565  crossref  mathscinet  zmath  isi  scopus
    6. Thomas S., “A Descriptive View of Combinatorial Group Theory”, Bull Symbolic Logic, 17:2 (2011), 252–264  crossref  mathscinet  zmath  isi  scopus
    7. Calderoni F., Thomas S., “The Bi-Embeddability Relation For Countable Abelian Groups”, Trans. Am. Math. Soc., 371:3 (2019), 2237–2254  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:332
    Full text:94
    References:36
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020