OD elements of countable OD sets in the Solovay model

Abstract

It is true in the Solovay model that every countable ordinal-definable set of sets of reals contains only ordinal-definable elements.

20 pages with index

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• An unpublished theorem of Solovay, revisited