Skip to main content
SpringerLink
Log in

A Cantor-Bernstein Theorem for σ-Complete MV-Algebras

  • Published:
Czechoslovak Mathematical Journal Aims and scope Submit manuscript

Abstract

The Cantor-Bernstein theorem was extended to σ-complete boolean algebras by Sikorski and Tarski. Chang's MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Lukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to σ-complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.

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. R. Cignoli and D. Mundici: An invitation to Chang's MV-algebras. In: Advances in Algebra and Model Theory (M. Droste, R. Göbel, eds.). Gordon and Breach Publishing Group, Reading, UK, 1997, pp. 171-197.

    Google Scholar 

  2. R. Cignoli, I. M. L. D'Ottaviano and D. Mundici: Algebraic Foundations of Many-valued Reasoning. Trends in Logic. Vol. 7. Kluwer Academic Publishers, Dordrecht, 1999.

    Google Scholar 

  3. W. Hanf: On some fundamental problems concerning isomorphism of boolean algebras. Math. Scand. 5 (1957), 205-217.

    Google Scholar 

  4. J. Jakubík: Cantor-Bernstein theorem for MV-algebras. Czechoslovak Math. J. 49(124) (1999), 517-526.

    Google Scholar 

  5. S. Kinoshita: A solution to a problem of Sikorski. Fund. Math. 40 (1953), 39-41.

    Google Scholar 

  6. A. Levy: Basic Set Theory. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1979.

    Google Scholar 

  7. D. Mundici: Interpretation of AF C*-algebras in Lukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15-63.

    Google Scholar 

  8. R. Sikorski: Boolean Algebras. Springer-Verlag. Ergebnisse Math. Grenzgeb., Berlin, 1960.

    Google Scholar 

  9. R. Sikorski: A generalization of a theorem of Banach and Cantor-Bernstein. Colloq. Math. 1 (1948), 140-144 and 242.

    Google Scholar 

  10. A. Tarski: Cardinal Algebras. Oxford University Press, New York, 1949.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, Via Cintia, 80126, Napoli, Italy

    A. De Simone

  2. Department of Mathematics, University of Florence, Viale Morgagni 67/A, 50134, Florence, Italy

    D. Mundici

  3. Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27, Praha 6, Czech Republic

    M. Navara

Authors
  1. A. De Simone
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Mundici
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Navara
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

De Simone, A., Mundici, D. & Navara, M. A Cantor-Bernstein Theorem for σ-Complete MV-Algebras. Czechoslovak Mathematical Journal 53, 437–447 (2003). https://doi.org/10.1023/A:1026299723322

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1026299723322

Search

Navigation