Abstract
We prove that it is true in Sacks, Cohen, and Solovay generic extensions that any ordinal definable Borel set of reals necessarily contains an ordinal definable element. This result has previously been known only for countable sets.
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The authors wish to express gratitude to the anonymous referee for valuable remarks, which have allowed us to supplement and improve the presentation.
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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 105, No. 5, pp. 696–707.
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Kanovei, V.G., Lyubetsky, V.A. Definable Elements of Definable Borel Sets. Math Notes 105, 684–693 (2019). https://doi.org/10.1134/S0001434619050055
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DOI: https://doi.org/10.1134/S0001434619050055