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Mat. Zametki, 2019, Volume 105, Issue 5, Pages 696–707 (Mi mz12001)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00705
Russian Science Foundation 18-29-13037
This work was supported in part by the Russian Foundation for Basic Research under grants 17-01-00705 (V. G. Kanovei) and 18-29-13037 (V. A. Lyubetsky).


DOI: https://doi.org/10.4213/mzm12001

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

Document Type: Article
UDC: 510.225+510.223
Received: 16.03.2018
Revised: 09.09.2018

Citation: V. G. Kanovei, V. A. Lyubetskii, “Definable Elements of Definable Borel Sets”, Mat. Zametki, 105:5 (2019), 696–707; Math. Notes, 105:5 (2019), 684–693

Citation in format AMSBIB
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\paper Definable Elements of Definable Borel Sets
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\issue 5
\pages 696--707
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\transl
\jour Math. Notes
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\pages 684--693
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