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Zap. Nauchn. Sem. POMI, 2008, Volume 358, Pages 189–198 (Mi znsl2151)  

Borel reducibility as an additive property of domains

V. G. Kanovei, V. A. Lyubetskii

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: We prove that under certain requirements if $\mathrm E$ and $\mathrm F$ are Borel equivalence relations, $X=\bigcup_nX_n$ is a countable union of Borel sets, and $\mathrm E\upharpoonright X_n$ is Borel reducible to $\mathrm F$ for all $n$ then $\mathrm E\upharpoonright X$ is Borel reducible to $\mathrm F$. Thus the property of Borel reducibility to $\mathrm F$ is countably additive as a property of domains. Bibl. – 18 titles.

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English version:
Journal of Mathematical Sciences (New York), 2009, 158:5, 708–712

UDC: 510.225
Received: 10.04.2007

Citation: V. G. Kanovei, V. A. Lyubetskii, “Borel reducibility as an additive property of domains”, Studies in constructive mathematics and mathematical logic. Part XI, Zap. Nauchn. Sem. POMI, 358, POMI, St. Petersburg, 2008, 189–198; J. Math. Sci. (N. Y.), 158:5 (2009), 708–712

Citation in format AMSBIB
\Bibitem{KanLyu08}
\by V.~G.~Kanovei, V.~A.~Lyubetskii
\paper Borel reducibility as an additive property of domains
\inbook Studies in constructive mathematics and mathematical logic. Part~XI
\serial Zap. Nauchn. Sem. POMI
\yr 2008
\vol 358
\pages 189--198
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl2151}
\elib{http://elibrary.ru/item.asp?id=13622783}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2009
\vol 158
\issue 5
\pages 708--712
\crossref{https://doi.org/10.1007/s10958-009-9406-2}
\elib{http://elibrary.ru/item.asp?id=13608054}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349232744}


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