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A definable E 0 class containing no definable elements

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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.

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Authors and Affiliations

  1. Institute for Information Transmission Problems (IITP), Bolshoy Karetny, 19, Moscow, 127051, Russia

    Vladimir Kanovei & Vassily Lyubetsky

  2. Moscow State University of Railway Engineering (MIIT), Novosushevskaya, 22, Moscow, 127994, Russia

    Vladimir Kanovei

Authors
  1. Vladimir Kanovei
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  2. Vassily Lyubetsky
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Corresponding author

Correspondence to Vladimir Kanovei.

Additional information

The work of Vladimir Kanovei was supported by RFFI Grant 13-01-00006.

The work of Vassily Lyubetsky was supported by the Russian Scientific Fund (Grant No. 14-50-00150).

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Kanovei, V., Lyubetsky, V. A definable E 0 class containing no definable elements. Arch. Math. Logic 54, 711–723 (2015). https://doi.org/10.1007/s00153-015-0436-9

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  • DOI: https://doi.org/10.1007/s00153-015-0436-9

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