A definable ${\mathsf{E}}_0$-class containing no definable elements

Abstract

A generic extension $L[x]$ of $L$ by a real $x$ is defined, in which the ${\mathsf{E}}_0$-class of $x$ is a lightface ${\Pi }_2^1$ set containing no ordinal-definable reals.

arXiv admin note: substantial text overlap with arXiv:1408.3901

Cited by in corpus (5)

• Definable ${\mathsf{E}}_0$ classes at arbitrary projective levels
• Counterexamples to countable-section ${\Pi }_2^1$ uniformization and ${\Pi }_3^1$ separation
• Countable OD sets of reals belong to the ground model
• In Cohen generic extension, every countable OD set of reals belongs to the ground model
• OD elements of countable OD sets in the Solovay model