×

zbMATH — the first resource for mathematics

Representations of monadic MV-algebras. (English) Zbl 1093.06008
Summary: Representations of monadic MV-algebras, the characterization of locally finite monadic MV-algebras, with axiomatization of them, and definability of non-trivial monadic operators on finitely generated free MV-algebras are given. Moreover, it is shown that the finitely generated \(m\)-relatively complete subalgebras of finitely generated free MV-algebras are projective.

MSC:
06D35 MV-algebras
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] 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 · Zbl 0121.01203
[2] Belluce, L. P., ’Further results on infinite valued predicate logic’, The Journal of Symbolic Logic 29, No 2 (1964), 69–78. · Zbl 0127.00801
[3] Belluce, L. P., Di Nola, A., Lettieri, A. ’Local MV-algebras’, Rendiconti Circolo Matematico di Palermo, Serie II. Tomo XLII, (1993), 347–361.
[4] Birkhoff, G., ’Lattice Theory’, Providence, Rhode Island, 1967. · Zbl 0153.02501
[5] Chang, C. C., ’Algebraic Analysis of Many-Valued Logics’, Trans. Amer. Math. Soc. 88 (1958), 467–490. · Zbl 0084.00704
[6] 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. · Zbl 0964.06010
[7] Di Nola, A., and R. Grigolia, ’Projective MV -Algebras and Their Automorphism Groups’, J. of Multi-Valued Logic & Soft Computing 9 (2003), 291–317. · Zbl 1045.06004
[8] Di Nola, A., and R. Grigolia, ’On monadic MV -algebras’, APAL, to appear. · Zbl 1052.06010
[9] Di Nola, A., and A. Lettieri, ’Perfect MV -algebras are categorically equivalent to abelian l -groups’, Studia Logica 53, No. 3 (1994), 417–432. · Zbl 0812.06010
[10] Georgescu, G., Iurgulescu, A., and I. Leustean, ’Monadic and Closure MV Algebras’, Multi. Val. Logic 3 (1998), 235–257. · Zbl 0920.06004
[11] Grigolia, R., ’Algebraic analysis of Łukasiewicz-Tarski n-valued logical systems’, Selected Papers on Łukasiewicz Sentential Calculi, Wrocfiaw, 1977, pp. 81–91.
[12] Hay, L. S., An axiomatization of the infinitely many-valued calculus, M.S.Thesis at Cornell University, 1958.
[13] 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. · JFM 57.1319.01
[14] Mangani, P., ’On certain algebras related to many-valued logics’, Boll. Un. Mat. Ital. 4, 8 (1973), 68–78.
[15] Mundici, D., ’Interpretation of AF C* -Algebras in Łukasiewicz Sentential Calculus’, J. Funct. Analysis 65 (1986), 15–63. · Zbl 0597.46059
[16] Mundici, D., ’Averaging the Truth-value in Łukasiewicz Logic’, Studia Logica 55 (1995), 113–127. · Zbl 0836.03016
[17] Rutledge, J. D., ’A preliminary Investigation of the infinitely many-valued predicate calculus’, Ph.D. Thesis at Cornell University, 1959.
[18] Segerberg, K., An essay in classical modal logic, Uppsala, 1971. · Zbl 0311.02028
[19] Scarpellini, B., ’Die Nichaxiomatisierbarkeit des unendlichwertigen Pradikatenkalkulus von Łukasiewicz’, The Journal of Symbolic Logic 27 (1962),159–170. · Zbl 0112.24503
[20] Schwartz, D., ’Theorie der polyadischen MV-Algebren endlicher Ordnung’, Math. Nachr. 78 (1977), 131–138. 144 L. P. Belluce, R. Grigolia, A. Lettieri · Zbl 0402.03054
[21] Schwartz, D., ’Polyadic MV-algebras’, Zeit. f. math. Logik und Grundlagen d. Math. 26 (1980), 561–564. · Zbl 0488.03035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.