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Archive for Mathematical Logic

, Volume 57, Issue 3–4, pp 285–298 | Cite as

Countable OD sets of reals belong to the ground model

  • Vladimir Kanovei
  • Vassily Lyubetsky
Article
  • 29 Downloads

Abstract

It is true in the Cohen, Solovay-random, dominaning, and Sacks generic extension, that every countable ordinal-definable set of reals belongs to the ground universe. It is true in the Solovay collapse model that every non-empty OD countable set of sets of reals consists of \(\text {OD}\) elements.

Keywords

Countable sets Ordinal definability Generic extensions 

Mathematics Subject Classification

03E15 03E35 

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Copyright information

© Springer-Verlag GmbH Germany 2017

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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