Abstract
In this paper we show that the quasivariety generated by an infinite simple MV-algebra only depends on the rationals which it contains. We extend this property to arbitrary families of simple MV-algebras.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bell, J. L., and A. B. Slomson, Models and Ultraproducts: an Introduction, North-Holland Amsterdam, 1971.
Blok, W. J., and I. M. A. Ferrerim, ‘Hoops and their implicational reducts’ (abstract), Algebraic Methods in Logic and in Computer Science, Banach Center Publications 28 (1993), 219–230.
Burris S., and H. P. Sankappanavar, A course in Universal Algebra, Springer Verlag, New York, 1981.
Chang, C. C., ‘Algebraic analysis of many-valued logics’, Trans. Amer. Math. Soc. 88 (1958), 467–490.
Chang, C. C., ‘A new proof of the completeness of the Łukasiewicz axioms’, Trans. Amer. Math. Soc. 93 (1959), 74–80.
Cignoli, R., I. M. L. D'Ottaviano and D. Mundici, Algebras das Logicas de Łukasiewicz, UNICAMP, Brasil, 1994.
Cornish, W. H., ‘Varieties generated by finite BCK-algebras’, Bull. Austral. Math. Soc. 22 (1980), 411–413.
Di Nola, A., ‘Representation and reticulation by quotients of MV-algebras’, Ricerche Mat. 40 (1991), 291–297.
Di Nola, A., and A. Lettieri, ‘Equational Characterization of all Varieties of MV-algebras’ (submitted).
Font, J. M., A. J. Rodriguez and A. Torrens, Wajsberg algebras, Stochastica 8 (1984), n. 1, 5–31.
Hudson, J. F. P., Piecewise linear topology, W. Benjamin, New York, 1969.
Komori, Y., ‘Super-Łukasiewicz Propositional Logic’, Nagoya Math. J. 84 (1981), 119–133.
McNaughton, R., ‘A theorem about infinite-valued statement calculi’, JSL 16 (1951), 1–13.
Mundici, D., ‘Interpretation of AF C*-algebras in Łukasiewicz Sentential Calculus’, J. Funcl. Anal. 65 (1986), 15–63.
Newman, M., Integral Matrices, Academic Press, New York, 1972.
Rodriguez, A. J., and A. Torrens, ‘Wajsberg algebras and Post algebras’, Studia Logica 53 (1994), 1–19.
Torrens, A., Cyclic elements in MV-algebras and Post algebras, Math. Log. Quart. 40 (1994), 431–444.
WÓjcicki, R., ‘On matrix representations of consequence operations of Łukasiewicz's sentential calculi’, ZML 19 (1976), 239–247.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Gispert, J., Torrens, A. Quasivarieties Generated by Simple MV-algebras. Studia Logica 61, 79–99 (1998). https://doi.org/10.1023/A:1005034431377
Issue Date:
DOI: https://doi.org/10.1023/A:1005034431377