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 Tr. Mat. Inst. Steklova, 2006, Volume 252, Pages 94–113 (Mi tm65)

A Cofinal Family of Equivalence Relations and Borel Ideals Generating Them

V. G. Kanovei, V. A. Lyubetskii

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: An increasing $\omega _1$-sequence of Borel equivalence relations on a Polish space that is cofinal (in the sense of Borel reducibility) in the family of all Borel equivalence relations is defined as a development of Rosendal's construction. It is proved that equivalence relations from this sequence are generated by explicitly defined Borel ideals.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2006, 252, 85–103

Bibliographic databases:

UDC: 510.225

Citation: V. G. Kanovei, V. A. Lyubetskii, “A Cofinal Family of Equivalence Relations and Borel Ideals Generating Them”, Geometric topology, discrete geometry, and set theory, Collected papers, Tr. Mat. Inst. Steklova, 252, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 94–113; Proc. Steklov Inst. Math., 252 (2006), 85–103

Citation in format AMSBIB
\Bibitem{KanLyu06} \by V.~G.~Kanovei, V.~A.~Lyubetskii \paper A~Cofinal Family of Equivalence Relations and Borel Ideals Generating Them \inbook Geometric topology, discrete geometry, and set theory \bookinfo Collected papers \serial Tr. Mat. Inst. Steklova \yr 2006 \vol 252 \pages 94--113 \publ Nauka, MAIK «Nauka/Inteperiodika» \publaddr M. \mathnet{http://mi.mathnet.ru/tm65} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2255972} \transl \jour Proc. Steklov Inst. Math. \yr 2006 \vol 252 \pages 85--103 \crossref{https://doi.org/10.1134/S008154380601010X} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746072961}