Geodesic
Borel reducibility as an additive property of domains
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XI, Tome 358 (2008), pp. 189-198

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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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     title = {Borel reducibility as an additive property of domains},
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     publisher = {mathdoc},
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     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_358_a9/}
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V. G. Kanovei; V. A. Lyubetskii. Borel reducibility as an additive property of domains. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XI, Tome 358 (2008), pp. 189-198. http://geodesic.mathdoc.fr/item/ZNSL_2008_358_a9/