Skip to main content
SpringerLink
Log in

The Priestley duality for Wajsberg algebras

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

The Priestley duality for Wajsberg algebras is developed. The Wajsberg space is a De Morgan space endowed with a family of functions that are obtained in rather natural way.

As a first application of this duality, a theorem about unicity of the structure is given.

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, Proper n-valued Łukasiewicz algebras as S-algebras of Łukasiewicz n-valued propositional calculi, Studia Logica XLI (1982), pp. 3–16.

    Google Scholar 

  2. R. Cignoli, manuscript.

  3. W. Cornish and P. Fowler, Coproducts of De Morgan algebras, Bulletin of the Australian Mathematical Society 16 (1977), pp. 1–13.

    Google Scholar 

  4. W. Cornish and P. Fowler, Coproducts of Kleene algebras, J. Austral. Math. Soc. Ser A 27, pp. 209–220.

  5. C. C. Chang, Algebraic Analysis of many valued logics, Transactions of the American Mathematical Society 88 (1958), pp. 467–490.

    Google Scholar 

  6. C. C. Chang, A new proof of the completeness of the Łukasiewicz axioms, Transactions of the American Mathematical Society 93 (1959), pp. 74–80.

    Google Scholar 

  7. J. Font, A. Rodriguez and A. Torrens, Wajsberg algebras, Stochastica, vol. VIII, N∘ 1 (1984), pp. 5–31.

    Google Scholar 

  8. D. Gluschankof and N. Martinez: The Kleene structure does not determinate the Wajsberg implication. Comunication to the U.M.A. (1987).

  9. D. Gluschankof: Doctoral Thesis (in preparation). Fac. Cs. Exactas y Naturales, Universidad de Buenos Aires.

  10. R. S. Grigolia: Algebraic analysis of Łukasiewicz-Tarski n-valued logical systems, In Selected Papers on Łukasiewicz Sentential Calculi, Ryszard Wójcicki ed., Warszawa, 1974.

  11. Y. Komori, The separation theorem of the X 0-valued Łukasiewicz propositional logic, Rep. Fac. of Sc., Shizuoka University, vol. 12 (1978), pp. 1–5.

    Google Scholar 

  12. Y. Komori, Super Łukasiewicz implicational logics, Nagoya Math. J., vol. 72 (1978), pp. 127–133.

    Google Scholar 

  13. Y. Komori, Super Łukasiewicz implicational logics, Nagoya Math. J., vol. 84 (1981), pp. 119–133.

    Google Scholar 

  14. A. Monteiro: L'arithmetique des filtres et us espaces topologiques, Notas de Lógica mathemática, Univ. Nac. des Sur. 1974, pp. 29–30.

  15. D. Mundici: Interpretation of AF C *-algebras in Łukasiewicz Sentential Calculus, Journal of Functional Analysis, 65, N∘ 1, January 1986.

  16. H. A. Priestley: Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2, pp. 186–190.

  17. H. A. Priestley: Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. (3) 24, pp. 507–530.

  18. A. J. Rodriguez: Un estudio algebraico de los cálculas proposicionales de Łukasiewicz, Ph. D. Thesis. Universidad de Barcelona, 1980.

  19. A. Torrens, W-algebras which are boolean products of members of SR [1], Studia Logica 46 (1987), pp. 265–275.

    Google Scholar 

  20. T. Traczyk, On the variety of bounded conmutative BCK-algebras, Math. Jap., 24 3 (1979), pp. 283–292.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática Facultad de Cs. Exactas y Naturales, U.B.A. Pab. I Ciudad Universitaria, 1428, Nuñez-Buenos Aires, Argentina

    N. G. Martínez

Authors
  1. N. G. Martínez
    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

Martínez, N.G. The Priestley duality for Wajsberg algebras. Stud Logica 49, 31–46 (1990). https://doi.org/10.1007/BF00401552

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00401552

Keywords

Search

Navigation