A definable E 0 class containing no definable elements

Archive for Mathematical Logic 54 (5-6):711-723 (2015)

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Abstract
A generic extension L[x]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf{L}[x]}$$\end{document} by a real x is defined, in which the E0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{E}_0}$$\end{document}-class of x is a lightface Π21\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\it \Pi}^1_2}$$\end{document} set containing no ordinal-definable reals.
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DOI 10.1007/s00153-015-0436-9
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References found in this work BETA

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.

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Citations of this work BETA

DefinableE0classes at Arbitrary Projective Levels.Vladimir Kanovei & Vassily Lyubetsky - 2018 - Annals of Pure and Applied Logic 169 (9):851-871.
Ordinal Definability and Combinatorics of Equivalence Relations.William Chan - 2019 - Journal of Mathematical Logic 19 (2):1950009.

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