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 OD elements.
CITATION STYLE
Kanovei, V., & Lyubetsky, V. (2018). Countable OD sets of reals belong to the ground model. Archive for Mathematical Logic, 57(3–4), 285–298. https://doi.org/10.1007/s00153-017-0569-0
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