A Duality for (n+1)-valued MV-algebras

• Autorzy: Lattanzi M. , Petrovich A.
• Języki publikacji: EN

Abstrakty

EN

MV -algebras were introduced by Chang to prove the completeness of the infinite-valued Lukasiewicz propositional calculus. In this paper we give a categorical equivalence between the varieties of (n + 1)-valued MV-algebras and the classes of Boolean algebras endowed with a certain family of filters. An- other similar categorical equivalence is given by A. Di Nola and A. Lettieri. Also, we point out the relations between this categor- ical equivalence and the duality established by R. Cignoli, which can be derived from results obtained by P. Niederkorn on natural dualities for varieties of MV -algebras.

• Wydawca: Wydawnictwo Uniwersytetu Jagiellońskiego
• Czasopismo: Reports on Mathematical Logic
• Rocznik: 2009
• Tom: Vol. 44
• Strony: 65--84
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Lattanzi M.

autor

Petrovich A.

• Departamento de Matem´atica - Facultad de Ciencias Exactas y Naturales Universidad Nacional de La Pampa Av. Uruguay 151 - (6300) Santa Rosa, La Pampa, Argentina,

Bibliografia

• [1] V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, Łukasiewicz–Moisil Algebras, North–Holland, 1991.
• [2] S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Graduate texts in Mathematics 78, Springer Verlag, New York, 1981.
• [3] C.C. Chang, Algebraic analysis of many valued logics, Transactions of the American Mathematical Society 88 (1958), pp. 467–490.
• [4] C.C. Chang, A new proof of the completeness of the Łukasiewicz axioms, Transactions of the American Mathematical Society 93 (1959), pp. 74–80.
• [5] R. Cignoli, Natural dualities for the algebras of Łukasiewicz finitely-valued logics, The Bulletin of Symbolic Logic 2 (1996), pp. 218.
• [6] R.L.O. Cignoli, I.M.L. D’Ottaviano and D. Mundici, Algebraic Foundations of Many-vlued Reasoning, Kluwer Academic Publishers, 2000.
• [7] A. Di Nola and A. Lettieri, One Chain Generated Varieties of MV-Algebras, Journal of Algebra 225 (2000), pp. 667–697.
• [8] J.M. Font, A.J. Rodriguez and A. Torrens, Wajsberg algebras, Stochastica 8 (1984), pp. 5–31.
• [9] R.S. Grigolia, Algebraic analysis of Łukasiewicz-Tarski’s n−valued logical systems, in R. Wójcicki, G. Malinowski (Eds.) Selected Papers on Łukasiewicz Sentential Calculi, Ossolineum, Wroclaw (1977), pp. 81–92.
• [10] A. Iorgulescu, Connections between MVn algebras and n−valued Łukasiewicz–Moisil algebras Part II, Discrete Mathematics 202, 1–3 (1999), pp. 113–134.
• [11] K. Keimel and H. Werner, Stone duality for varieties generated by a quasi-primal algebra, Mem. Amer. Math. Soc. 148 (1974), pp. 59–85.
• [12] Y. Komori, The separation theorem of the N0−valued Lukasiewicz propositional logic, Reports of the Faculty of Sciences, Shizuoka University 12 (1978), pp. 1–5.
• [13] N. G. Martínez, The Priestley Duality for Wajsberg Algebras, Studia Logica 49, 1 (1990), pp. 31–46.
• [14] P. Niederkorn, Natural Dualities for Varieties of MV-algebras, I, Journal of Mathematical Analysis and Applications 255 (2001), pp. 58–73.
• [15] A.J. Rodríguez, Un estudio algebraico de los Cálculos Proposicionales de Lukasiewicz, Tesis Doctoral, Univ. de Barcelona, 1980.
• [16] A. J. Rodríguez and A. Torrens, Wajsberg Algebras and Post Algebras, Studia Logica 53 (1994), pp. 1–19.