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Matematicheskie Zametki, 2019, Volume 105, Issue 5, Pages 696–707
DOI: https://doi.org/10.4213/mzm12001 (Mi mzm12001) 		 
This article is cited in 1 scientific paper (total 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
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DOI: https://doi.org/10.4213/mzm12001
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).
Received: 16.03.2018
Revised: 09.09.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 5, Pages 684–693
DOI: https://doi.org/10.1134/S0001434619050055
Bibliographic databases:
Document Type: Article
UDC: 510.225+510.223
Language: Russian
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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    • This publication is cited in the following 1 articles:
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