Siberian Mathematical Journal

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

A Generic Property of the Solovay Set Σ



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.


genericity Solovay set Σ 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  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).MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Kanoveĭ V. G. and Lyubetskiĭ V. A., Modern Set Theory: Absolutely Unsolvable Classical Problems [Russian], MTsNMO, Moscow (2013).MATHGoogle Scholar
  3. 3.
    Grigorieff S., “Intermediate submodels and generic extensions of set theory,” Ann. Math., vol. 101, 447–490 (1975).MathSciNetCrossRefMATHGoogle 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).MathSciNetCrossRefMATHGoogle 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).MATHGoogle 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).MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Zapletal J., “Terminal notions in set theory,” Ann. Pure Appl. Logic, vol. 109, no. 1–2, 89–116 (2001).MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

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

Personalised recommendations