Advertisement

Siberian Mathematical Journal

, Volume 58, Issue 6, pp 1012–1014 | Cite as

A Generic Property of the Solovay Set Σ

  • V. G. Kanovei
  • V. A. Lyubetsky
Article
  • 15 Downloads

Abstract

We prove that the Solovay set Σ is generic over the ground model in the sense of a forcing whose order relation extends the order relation of the given forcing.

Keywords

genericity Solovay set Σ 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Solovay R. M., “A model of set theory in which every set of reals is Lebesgue measurable,” Ann. Math., vol. 92, 1–56 (1970).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Kanoveĭ V. G. and Lyubetskiĭ V. A., Modern Set Theory: Absolutely Unsolvable Classical Problems [Russian], MTsNMO, Moscow (2013).zbMATHGoogle Scholar
  3. 3.
    Grigorieff S., “Intermediate submodels and generic extensions of set theory,” Ann. Math., vol. 101, 447–490 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Fuchs G., Hamkins J. D., and Reitz J., “Set-theoretic geology,” Ann. Pure Appl. Logic, vol. 166, no. 4, 464–501 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Jech T., Set Theory. The Third Millennium Revised and Expanded, Springer-Verlag, Berlin, Heidelberg, and New York (2003).Google Scholar
  6. 6.
    Kanamori A., The Higher Infinite. Large Cardinals in Set Theory from Their Beginnings, Springer, Berlin (2003).zbMATHGoogle Scholar
  7. 7.
    Kanoveĭ V. G. and Lyubetsky V. A., “Generalization of one construction by Solovay,” Sib. Math. J., vol. 56, no. 6, 1072–1079 (2015).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Zapletal J., “Terminal notions in set theory,” Ann. Pure Appl. Logic, vol. 109, no. 1–2, 89–116 (2001).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsRussian University of TransportMoscowRussia

Personalised recommendations