Geodesic
Definable Elements of Definable Borel Sets
Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 696-707

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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.
Mots-clés : definable elements
Keywords: Borel sets, Cohen forcing, Solovay forcing. 
@article{MZM_2019_105_5_a4,
     author = {V. G. Kanovei and V. A. Lyubetskii},
     title = {Definable {Elements} of {Definable} {Borel} {Sets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {696--707},
     publisher = {mathdoc},
     volume = {105},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a4/}
}
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V. G. Kanovei; V. A. Lyubetskii. Definable Elements of Definable Borel Sets. Matematičeskie zametki, Tome 105 (2019) no. 5, pp. 696-707. http://geodesic.mathdoc.fr/item/MZM_2019_105_5_a4/