Skip to main content
SpringerLink
Log in

The Theories of Superatomic Boolean Algebras with Distinguished Subalgebra Which Lack Countably Saturated Models

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

Studying Boolean algebras with distinguished subalgebras, we establish the existence of continuum many simple superatomic Boolean algebras with distinguished subalgebra whose elementary theories are distinct and each of them lacks countably saturated models. The subalgebras coincide with the Boolean algebras modulo their Fréchet ideals.

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.

Similar content being viewed by others

References

  1. Chang C. C. and Keisler H. J., Model Theory, North-Holland, Amsterdam and London (1973).

    MATH  Google Scholar 

  2. Goncharov S. S., Countable Boolean Algebras and Decidability [Russian], Nauchnaya Kniga, Novosibirsk (1997).

    MATH  Google Scholar 

  3. Palchunov D. E., “Undecidability of theories of Boolean algebras with selected ideals,” Algebra and Logic, vol. 25, no. 3, 206–219 (1986).

    Article  MathSciNet  Google Scholar 

  4. Palchunov D. E., “Countably-categorical Boolean algebras with distinguished ideals,” Studia Logica, vol. XLVI, no. 2, 121–135 (1987).

    Article  MathSciNet  Google Scholar 

  5. Palchunov D. E., “Finitely axiomatizable Boolean algebras with distinguished ideals,” Algebra and Logic, vol. 26, no. 4, 252–266 (1987).

    Article  MathSciNet  Google Scholar 

  6. Palchunov D. E., “Direct summands of Boolean algebras with distinguished ideals,” Algebra and Logic, vol. 31, no. 5, 295–316 (1992).

    Article  MathSciNet  Google Scholar 

  7. Palchunov D. E., “Prime and countably saturated models of the theory of Boolean algebras with distinguished ideals,” Tr. Inst. Mat. (Novosibirsk), vol. 25, 82–103 (1993).

    MathSciNet  Google Scholar 

  8. Palchunov D. E., “The theory of Boolean algebras with distinguished ideals without a prime model,” Tr. Inst. Mat. (Novosibirsk), vol. 25, 104–132 (1993).

    MathSciNet  Google Scholar 

  9. Palchunov D. E., Trofimov A. V., and Turko A. I., “Autostability relative to strong constructivizations of Boolean algebras with distinguished ideals,” Sib. Math. J., vol. 56, no. 3, 490–498 (2015).

    Article  MathSciNet  Google Scholar 

  10. Palchunov D. E. and Trofimov A. V., “Local and nonvanishing superatomic Boolean algebras with a distinguished dense subalgebra,” Algebra and Logic, vol. 50, no. 6, 553–569 (2011).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    D. E. Palchunov & A. V. Trofimov

Authors
  1. D. E. Palchunov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. V. Trofimov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to D. E. Palchunov or A. V. Trofimov.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 654–668.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Palchunov, D.E., Trofimov, A.V. The Theories of Superatomic Boolean Algebras with Distinguished Subalgebra Which Lack Countably Saturated Models. Sib Math J 61, 516–527 (2020). https://doi.org/10.1134/S0037446620030131

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446620030131

Keywords

Search

Navigation