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Countable OD sets of reals belong to the ground model
Archive for Mathematical Logic 57 (3-4):285-298 (2018)
Abstract
It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension, that every countable ordinal-definable set of reals belongs to the ground universe. It is true in the Solovay collapse model that every non-empty OD countable set of sets of reals consists of \ elements.Author's Profile
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Citations of this work
The full basis theorem does not imply analytic wellordering.Vladimir Kanovei & Vassily Lyubetsky - 2021 - Annals of Pure and Applied Logic 172 (4):102929.
Typicality à la Russell in Set Theory.Athanassios Tzouvaras - 2022 - Notre Dame Journal of Formal Logic 63 (2).
An unpublished theorem of Solovay on OD partitions of reals into two non-OD parts, revisited.Ali Enayat & Vladimir Kanovei - 2020 - Journal of Mathematical Logic 21 (3):2150014.
References found in this work
A definable E 0 class containing no definable elements.Vladimir Kanovei & Vassily Lyubetsky - 2015 - Archive for Mathematical Logic 54 (5-6):711-723.
Set Theory: On the Structure of the Real Line.T. Bartoszyński & H. Judah - 1999 - Studia Logica 62 (3):444-445.
An Ulm-type classification theorem for equivalence relations in Solovay model.Vladimir Kanovei - 1997 - Journal of Symbolic Logic 62 (4):1333-1351.
On coding uncountable sets by reals.Joan Bagaria & Vladimir Kanovei - 2010 - Mathematical Logic Quarterly 56 (4):409-424.
Unbounded and dominating reals in Hechler extensions.Justin Palumbo - 2013 - Journal of Symbolic Logic 78 (1):275-289.
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