Countable OD sets of reals belong to the ground model

Abstract

It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension that every countable ordinal-definable set of reals belongs to to the ground universe

16 pages

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
• On countable cofinality of definable chains in Borel partial orders

Cited by in corpus (2)

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• An unpublished theorem of Solovay, revisited