Siberian Mathematical Journal

, Volume 56, Issue 6, pp 1072–1079 | Cite as

Generalization of one construction by Solovay

  • V. G. Kanovei
  • V. A. Lyubetsky


The well-known Σ-construction in forcing by Solovay is generalized to the case of intermediate sets that are not subsets of the initial model. Our method gives a more transparent construction of a forcing over an intermediate model than that in the classical paper [1] by Grigorieff on intermediate models.


intermediate model sigma-construction forcing 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Grigorieff S., “Intermediate submodels and generic extensions of set theory,” Ann. Math., 101, 447–490 (1975).zbMATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    Solovay R. M., “A model of set theory in which every set of reals is Lebesgue measurable,” Ann. Math., 92, 1–56 (1970).zbMATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Kanovei V. G. and Lyubetsky V. A., Modern Set Theory: Borel and Projective Sets [in Russian], MTsNMO, Moscow (2013).Google Scholar
  4. 4.
    Kanovei V. G. and Lyubetsky V. A., “An effective minimal encoding of uncountable sets,” Siberian Math. J., 52, No. 5, 854–863 (2011).zbMATHCrossRefGoogle Scholar
  5. 5.
    Kanovei V., Borel Equivalence Relations: Structure and Classification, Amer. Math. Soc., New York (2008) (Univ. Lect. Ser. Amer. Math. Soc.; V. 44).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsInstitute of Economics and FinanceMoscowRussia
  2. 2.Institute for Information Transmission Problems MoscowMoscowRussia

Personalised recommendations