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A characterization of MV-algebras free over finite distributive lattices

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Abstract

Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.

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References

  1. Aguzzoli S., Mundici D.: An algorithmic desingularization of 3-dimensional toric varieties. Tohoku Math. J. (2) 46(4), 557–572 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bayer M.M.: Barycentric subdivisions. Pac. J. Math. 135(1), 1–16 (1988)

    MathSciNet  MATH  Google Scholar 

  3. Beynon W.M.: Vector lattices freely generated by distributive lattices. Math. Proc. Camb. Philos. Soc. 81(2), 193–200 (1977)

    Article  MathSciNet  MATH  Google Scholar 

  4. Björner, A.: Topological Methods. In: Handbook of combinatorics, vol. 1, 2, pp. 1819–1872. Elsevier, Amsterdam (1995)

  5. Bouvier C., Gonzalez-Sprinberg G.: Système générateur minimal, diviseurs essentiels et G-désingularisations de variétés toriques. Tohoku Math. J. (2) 47(1), 125–149 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cignoli R.L.O., D’Ottaviano I.M.L., Mundici D.: Algebraic Foundations of Many-Valued Reasoning. Kluwer, Dordrecht (2000)

    MATH  Google Scholar 

  7. Hájek P.: Metamathematics of Fuzzy Logic. Kluwer, Dordrecht (1998)

    MATH  Google Scholar 

  8. Johnstone P.T.: Stone Spaces. Cambridge University Press, Cambridge (1982)

    MATH  Google Scholar 

  9. Marra V., Mundici D.: The Lebesgue state of a unital abelian lattice-ordered group. J. Group Theory 10(5), 655–684 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mundici D.: Interpretation of AF C*-algebras in Łukasiewicz sentential calculus. J. Funct. Anal. 65(1), 15–63 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Mundici D.: Farey stellar subdivisions, ultrasimplicial groups, and K 0 of AF C*-algebras. Adv. Math. 68(1), 23–39 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  12. Mundici D.: A characterization of the free n-generated MV-algebra. Arch. Math. Log. 45(2), 239–247 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Panti G.: A geometric proof of the completeness of the Łukasiewicz calculus. J. Symb. Log. 60(2), 563–578 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rourke C.P., Sanderson B.J.: Introduction to piecewise-linear topology. Springer, Berlin (1982)

    MATH  Google Scholar 

  15. Semadeni Z.: Schauder bases in Banach spaces of continuous functions. Lecture Notes in Mathematics, vol. 918. Springer, Berlin (1982)

    Google Scholar 

Download references

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  1. Dipartimento di Informatica e Comunicazione, Università degli Studi di Milano, via Comelico 39/41, 20135, Milano, Italy

    Vincenzo Marra

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  1. Vincenzo Marra
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Correspondence to Vincenzo Marra.

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Marra, V. A characterization of MV-algebras free over finite distributive lattices. Arch. Math. Logic 47, 263–276 (2008). https://doi.org/10.1007/s00153-008-0084-4

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  • DOI: https://doi.org/10.1007/s00153-008-0084-4

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