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Borel OD sets of reals are OD-Borel in some simple models


Authors: Vladimir Kanovei and Vassily Lyubetsky
Journal: Proc. Amer. Math. Soc. 147 (2019), 1277-1282
MSC (2010): Primary 03E35, 03E45
DOI: https://doi.org/10.1090/proc/14286
Published electronically: December 3, 2018
MathSciNet review: 3896073
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Abstract: It is true in the Cohen, Solovay-random, and Sacks generic extensions that every ordinal-definable Borel set of reals has a Borel code in the ground model, and hence if non-empty, then has an element in the ground model.


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Additional Information

Vladimir Kanovei
Affiliation: Institute for Information Transmission Problems, Russian Academy of Sciences
Email: kanovei@googlemail.com

Vassily Lyubetsky
Affiliation: Institute for Information Transmission Problems, Russian Academy of Sciences
Email: lyubetsk@iitp.ru

DOI: https://doi.org/10.1090/proc/14286
Received by editor(s): March 10, 2018
Received by editor(s) in revised form: June 14, 2018
Published electronically: December 3, 2018
Additional Notes: The first author acknowledges partial support of RFFI grant 17-01-00705
Vladimir Kanovei served as corresponding author.
The second author acknowledges partial support of Russian Scientific Fund grant 14-50-00150
Communicated by: Heike Mildenberger
Article copyright: © Copyright 2018 American Mathematical Society