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JOURNALS // Matematicheskie Zametki // Archive
Mat. Zametki, 2019 Volume 105, Issue 5, Pages 696–707 (Mi mzm12001)
This article is cited in 1 paper

Definable Elements of Definable Borel Sets

V. G. Kanovei, V. A. Lyubetskii

Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow

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.

Keywords: definable elements, Borel sets, Cohen forcing, Solovay forcing.

UDC: 510.225+510.223

Received: 16.03.2018
Revised: 09.09.2018

DOI: 10.4213/mzm12001


 English version: Mathematical Notes, 2019, 105:5, 684–693

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© Steklov Math. Inst. of RAS, 2025