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Zapiski Nauchnykh Seminarov POMI, 2008, Volume 358, Pages 189–198
(Mi znsl2151)
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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.
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
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https://www.mathnet.ru/eng/znsl2151 https://www.mathnet.ru/eng/znsl/v358/p189
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Abstract page: | 317 | Full-text PDF : | 102 | References: | 61 |
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