Skip to main content
SpringerLink
Log in

Boolean-Valued Universe as an Algebraic System. II: Intensional Hierarchies

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

Under study are the notions of transitivity, regularity, and σ-regularity for Boolean-valued algebraic systems of set-theoretic signature. The notion of a universe over an arbitrary extensional Boolean-valued system is introduced. Some description is proposed for the structure of the universe by means of various hierarchies. The results are used for proving the uniqueness of a Boolean-valued universe up to a unique isomorphism.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Gutman A. E., “Boolean-valued universe as an algebraic system. I: Basic principles,” Sib. Math. J., vol. 60, no. 5, 810–827 (2019).

    Article  Google Scholar 

  2. Jech T., Set Theory. The Third Millennium Edition, revised and expanded, Springer-Verlag, Berlin, etc. (2003).

    Google Scholar 

  3. Lévy A., A Hierarchy of Formulas in Set Theory, Amer. Math. Soc., Providence (1965).

    Book  Google Scholar 

  4. Kusraev A. G. and Kutateladze S. S., Introduction to Boolean Valued Analysis [Russian], Nauka, Moscow (2005).

    MATH  Google Scholar 

  5. Sikorski R., Boolean Algebras [Russian translation], Mir, Moscow (1969).

    Book  Google Scholar 

  6. Jech T., “Distributive laws,” in: Handbook of Boolean Algebras, North-Holland, Amsterdam and London, 1989. Chapter 8, 317–331.

    Google Scholar 

  7. Gutman A. E., “Locally one-dimensional K-spaces and σ-distributive Boolean algebras,” Sib. Adv. Math., vol. 5, no. 1, 42–48 (1995).

    MathSciNet  MATH  Google Scholar 

  8. Bourbaki N., Elements of Mathematics. Part 1. The Fundamental Structures of Analysis. Book 1. Theory of Sets [Russian translation], Mir, Moscow (1965).

    Google Scholar 

  9. Solovay R. M. and Tennenbaum S., “Iterated Cohen extensions and Souslin’s problem,” Ann. Math., vol. 94, no. 2, 201–245 (1971).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    A. E. Gutman

Authors
  1. A. E. Gutman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. E. Gutman.

Additional information

Dedicated to Yu. L. Ershov on the occasion of his 80th birthday.

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 539–571.

The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project 0314-2019-0005).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Gutman, A.E. Boolean-Valued Universe as an Algebraic System. II: Intensional Hierarchies. Sib Math J 61, 426–452 (2020). https://doi.org/10.1134/S0037446620030052

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446620030052

Keywords

Search

Navigation