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Mathematical Notes

, Volume 77, Issue 3–4, pp 307–310 | Cite as

Perfect subsets of invariant CA-sets

  • V. G. Kanovei
  • V. A. Lyubetskii
Article
  • 32 Downloads

Abstract

The familiar theorem that any Σ 2 1 (a)-set X of real numbers (where a is a fixed real parameter) not containing a perfect kernel necessarily satisfies the condition X\( \subseteq \)L[a] is extended to a wider class of sets, with countable ordinals allowed as additional parameters in Σ 2 1 (a)-definitions.

Key words

perfect kernel property perfect subset forcing descriptive set theory CA-set 

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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • V. G. Kanovei
    • 1
  • V. A. Lyubetskii
    • 1
  1. 1.Institute for Problems in Information TransmissionRussian Academy of SciencesRussia

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