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Archive for Mathematical Logic

, Volume 54, Issue 5–6, pp 711–723 | Cite as

A definable E 0 class containing no definable elements

  • Vladimir Kanovei
  • Vassily Lyubetsky
Article

Abstract

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

Keywords

Jensen reals Definable equivalence class Definable elements 

Mathematics Subject Classification

03E15 03E35 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institute for Information Transmission Problems (IITP)MoscowRussia
  2. 2.Moscow State University of Railway Engineering (MIIT)MoscowRussia

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