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Monadic MV-algebras are Equivalent to Monadic -groups with Strong Unit

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Abstract

In this paper we extend Mundici’s functor Γ to the category of monadic MV-algebras. More precisely, we define monadic -groups and we establish a natural equivalence between the category of monadic MV-algebras and the category of monadic -groups with strong unit. Some applications are given thereof.

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References

  1. Belluce L.P., Grigolia R., Lettieri A.: ‘Representations of Monadic MValgebras’. Studia Logica 81, 123–144 (2005)

    Article  Google Scholar 

  2. Chang C.C.: ‘Algebraic analysis of many valued logics’. Trans. Amer. Math. Soc. 88, 467–490 (1958)

    Article  Google Scholar 

  3. Chang C.C.: ‘A New Proof of the Completeness of the Łukasiewicz Axioms’. Trans. Amer. Math. Soc. 93, 74–80 (1959)

    Google Scholar 

  4. Cignoli, R., I. L. D’Ottaviano, and D. Mundici, Algebraic Foundations of Manyvalued Reasoning, Vol. 7 of Trends in Logic - Studia Logica Library, Kluwer Academic Publishers, Dordrecht, 2000.

  5. Cignoli, R., and D. Mundici, ‘An Invitation to Chang’s MV Algebras’, Advances in Algebra and Model Theory, Essen, 1994; Dresden, 1995, Algebra Logic Appl., 9, Gordon and Breach, Amsterdam, 171–197, 1997.

  6. Cignoli R., Mundici D.: ‘An Elementary Presentation of the Equivalence Between MV-algebras and -groups with Strong Unit’. Studia Logica 61, 49–64 (1998)

    Article  Google Scholar 

  7. Di Nola A., Grigolia R.: ‘On Monadic MV-algebras’. Annals of Pure and Applied Logic 128, 125–139 (2004)

    Article  Google Scholar 

  8. Lattanzi, M., and A. Petrovich, ‘A Duality for Monadic (n + 1)-valued MValgebras’, Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress, Univ. Nac. del Sur, Bahía Blanca, 107–117, 2008.

  9. Mundici D.: ‘Interpretation of FA C*-algebras in Łukasiewicz Sentential Calculus’. J. Funct. Anal. 65(1), 15–63 (1986)

    Article  Google Scholar 

  10. Rutledge, J. D., ‘A Preliminary Investigation of the Infinitely Many-valued Predicate Calculus’, Ph. D. Thesis, Cornell University, 1959.

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Correspondence to J. P. Díaz Varela.

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Cimadamore, C., Díaz Varela, J.P. Monadic MV-algebras are Equivalent to Monadic -groups with Strong Unit. Stud Logica 98, 175–201 (2011). https://doi.org/10.1007/s11225-011-9332-4

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  • DOI: https://doi.org/10.1007/s11225-011-9332-4

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