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Countable OD sets of reals belong to the ground model. (English) Zbl 06860714
Summary: 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.

MSC:
03E15 Descriptive set theory
03E35 Consistency and independence results
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