In Cohen generic extension, every countable OD set of reals belongs to the ground model

Abstract

It is true in the Cohen generic extension of L, the constructible universe, that every countable ordinal-definable set of reals belongs to L.

References in corpus (6)

• A definable ${\mathsf{E}}_0$-class containing no definable elements
• A countable definable set of reals containing no definable elements
• On countable cofinality and decomposition of definable thin orderings
• Linearization of partial quasi-orderings in the Solovay model revisited
• Bounding and decomposing thin analytic partial orderings
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Cited by in corpus (2)

• Typicality à la Russell in set theory
• An unpublished theorem of Solovay, revisited