Abstract
Representations of monadic MV -algebra, the characterization of locally finite monadic MV -algebras, with axiomatization of them, definability of non-trivial monadic operators on finitely generated free MV -algebras are given. Moreover, it is shown that finitely generated m-relatively complete subalgebra of finitely generated free MV -algebra is projective.
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Belluce, L. P., and C. C. Chang, ‘A weak completeness theorem for infinite valued first-order logic’, The Journal of Symbolic Logic 28, No 1 (1963), 43-50. Representations of monadic MV -algebras 143
Belluce, L. P., ‘Further results on infinite valued predicate logic’, The Journal of Symbolic Logic 29, No 2 (1964), 69–78.
Belluce, L. P., Di Nola, A., Lettieri, A. ‘Local MV-algebras’, Rendiconti Circolo Matematico di Palermo, Serie II. Tomo XLII, (1993), 347–361.
Birkhoff, G., ‘Lattice Theory’, Providence, Rhode Island, 1967.
Chang, C. C., ‘Algebraic Analysis of Many-Valued Logics’, Trans. Amer. Math. Soc. 88 (1958), 467–490.
Di Nola, A., Grigolia, R., and G. Panti, ‘Finitely generated free MV -algebras and their automorphism groups’, Studia Logica 61, No. 1 (1998), 65–78.
Di Nola, A., and R. Grigolia, ‘Projective MV -Algebras and Their Automorphism Groups’, J. of Multi-Valued Logic & Soft Computing 9 (2003), 291–317.
Di Nola, A., and R. Grigolia, ‘On monadic MV -algebras’, APAL, to appear.
Di Nola, A., and A. Lettieri, ‘Perfect MV -algebras are categorically equivalent to abelian l -groups’, Studia Logica 53, No. 3 (1994), 417–432.
Georgescu, G., Iurgulescu, A., and I. Leustean, ‘Monadic and Closure MV Algebras’, Multi. Val. Logic 3 (1998), 235–257.
Grigolia, R., ‘Algebraic analysis of Łukasiewicz-Tarski n-valued logical systems’, Selected Papers on Łukasiewicz Sentential Calculi, Wrocfiaw, 1977, pp. 81–91.
Hay, L. S., An axiomatization of the infinitely many-valued calculus, M.S.Thesis at Cornell University, 1958.
Łukasiewicz, J., and A. Tarski, ‘Unntersuchungen über den Aussagenkalkul’, Comptes Rendus des seances de la Societe des Sciences et des Lettres de Varsovie 23 (1930), cl iii, 30–50.
Mangani, P., ‘On certain algebras related to many-valued logics’, Boll. Un. Mat. Ital. 4, 8 (1973), 68–78.
Mundici, D., ‘Interpretation of AF C* -Algebras in Łukasiewicz Sentential Calculus’, J. Funct. Analysis 65 (1986), 15–63.
Mundici, D., ‘Averaging the Truth-value in Łukasiewicz Logic’, Studia Logica 55 (1995), 113–127.
Rutledge, J. D., ‘A preliminary Investigation of the infinitely many-valued predicate calculus’, Ph.D. Thesis at Cornell University, 1959.
Segerberg, K., An essay in classical modal logic, Uppsala, 1971.
Scarpellini, B., ‘Die Nichaxiomatisierbarkeit des unendlichwertigen Pradikatenkalkulus von Łukasiewicz’, The Journal of Symbolic Logic 27 (1962),159–170.
Schwartz, D., ‘Theorie der polyadischen MV-Algebren endlicher Ordnung’, Math. Nachr. 78 (1977), 131–138. 144 L. P. Belluce, R. Grigolia, A. Lettieri
Schwartz, D., ‘Polyadic MV-algebras’, Zeit. f. math. Logik und Grundlagen d. Math. 26 (1980), 561–564.
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Belluce, L.P., Grigolia, R. & Lettieri, A. Representations of monadic MV -algebras. Stud Logica 81, 123–144 (2005). https://doi.org/10.1007/s11225-005-2805-6
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DOI: https://doi.org/10.1007/s11225-005-2805-6