Skip to main content
Springer Nature Link
Log in

Duality Theory and Skeleta for Semisimple MV-Algebras

  • Published:
Studia Logica Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the \(\omega \)-skeleta of the MV-algebras are restricted in some way. In particular we consider antiskeletal MV-algebras, that is, the ones whose \(\omega \)-skeleton is trivial.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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. Cignoli, R., I.D. D’Ottaviano, and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Kluwer, 2000.

    Book  Google Scholar 

  2. Cignoli, R., E.J. Dubuc, and D. Mundici, Extending Stone duality to multisets and locally finite MV-algebras. J. Pure Appl. Algebra 189(1-3):37–59, 2004.

    Article  Google Scholar 

  3. Di Nola, A., G. Lenzi, and A.C. Russo, The skeletons of \(\ell \)-u groups and of MV-algebras, submitted.

  4. Marra, V., and L. Spada, The dual adjunction between mv-algebras and Tychonoff spaces. Studia Logica 100(1–2):253–278, 2012.

    Article  Google Scholar 

  5. Mundici, D., Advanced Łukasiewicz calculus and MV-algebras, Trends in Logic 35, Springer, 2011.

Download references

Acknowledgements

The authors thank Vincenzo Marra for useful discussions.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Salerno, Fisciano, Italy

    Antonio  Di  Nola & Giacomo Lenzi

  2. IIASS (Istituto Internazionale per gli Alti Studi Scientifici), Vietri sul Mare, SA, Italy

    Antonio  Di  Nola

Authors
  1. Antonio  Di  Nola
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Giacomo Lenzi
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Giacomo Lenzi.

Additional information

Presented by Jacek Malinowski; Received July 19, 2017.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

 Di  Nola, A., Lenzi, G. Duality Theory and Skeleta for Semisimple MV-Algebras. Stud Logica 106, 1239–1260 (2018). https://doi.org/10.1007/s11225-018-9787-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11225-018-9787-7

Keywords