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Zapiski Nauchnykh Seminarov 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
References:
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.
Received: 10.04.2007
English version:
Journal of Mathematical Sciences (New York), 2009, Volume 158, Issue 5, Pages 708–712
DOI: https://doi.org/10.1007/s10958-009-9406-2
Bibliographic databases:
UDC: 510.225
Language: Russian
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{https://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{https://elibrary.ru/item.asp?id=13608054}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-67349232744}
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  • https://www.mathnet.ru/eng/znsl2151
  • https://www.mathnet.ru/eng/znsl/v358/p189
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