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Keywords:
monadic $n$-valued Łukasiewicz algebra; monadic Boolean algebra; functional representation
monadic $n$-valued Łukasiewicz algebra; monadic Boolean algebra; functional representation
Summary:
Some functional representation theorems for monadic $n$-valued Łukasiewicz algebras (qLk$_{n}$-algebras, for short) are given. Bearing in mind some of the results established by G. Georgescu and C. Vraciu (Algebre Boole monadice si algebre Łukasiewicz monadice, Studii Cercet. Mat. 23 (1971), 1027–1048) and P. Halmos (Algebraic Logic, Chelsea, New York, 1962), two functional representation theorems for qLk$_{n}$-algebras are obtained. Besides, rich qLk$_{n}$-algebras are introduced and characterized. In addition, a third theorem for these algebras is presented and the relationship between the three theorems is shown.
References:
[1] Abad, M.: Estructuras cíclica y monádica de un álgebra de Łukasiewicz $n$-valente. Notas de Lógica Matemática 36. Inst. Mat. Univ. Nacional del Sur, Bahía Blanca, 1988. MR 0935965
[2] Balbes, R., Dwinger, P.: Distributive Lattices. Univ. of Missouri Press, Columbia, 1974. MR 0373985
[3] Bezhanishvili, G., Harding, J.: Functional monadic Heyting algebras. Algebra Universalis 48 (2002), 1–10. DOI 10.1007/s00012-002-8202-3 | MR 1930030
[4] Boicescu, C., Filipoiu, A., Georgescu, G., Rudeanu, S.: Łukasiewicz-Moisil Algebras. North-Holland, Amsterdam, 1991.
[5] Burris, S., Sankappanavar, H. P.: A Course in Universal Algebra. Graduate Texts in Mathematics, Vol. 78. Springer, Berlin, 1981. DOI 10.1007/978-1-4613-8130-3_3 | MR 0648287
[6] Cignoli, R.: Moisil Algebras. Notas de Lógica Matemática 27. Inst. Mat. Univ. Nacional del Sur, Bahía Blanca, 1970. MR 0345884 | Zbl 0212.31701
[7] Figallo, A. V., Pascual, I., Ziliani, A.: Notes on monadic $n$-valued Lukasiewicz algebras. Math. Bohem. 129 (2004), 255–271. MR 2092712
[8] Georgescu, G., Vraciu, C.: Algebre Boole monadice si algebre Łukasiewicz monadice. Studii Cercet. Mat. 23 (1971), 1025–1048. MR 0371650
[9] Halmos, P.: Algebraic Logic I. Monadic Boolean algebras. Compositio Math. 12 (1955), 217–249. MR 0078304
[10] Halmos, P.: Algebraic Logic. Chelsea, New York, 1962. MR 0131961 | Zbl 0101.01101
[11] Halmos, P.: Lectures on Boolean Algebra. Van Nostrand, Princeton, 1963. MR 0167440
[12] Kalman, J. A.: Lattices with involution. Trans. Amer. Math. Soc. 87 (1958), 485–491. DOI 10.1090/S0002-9947-1958-0095135-X | MR 0095135 | Zbl 0228.06003
[13] Moisil, Gr. C.: Notes sur les logiques non-chrysippiennes. Ann. Sci. Univ. Jassy 27 (1941), 86–98. MR 0018621 | Zbl 0025.29401
[14] Moisil, Gr. C.: Le algebre di Łukasiewicz. An. Univ. C.I. Parhon. Acta Logica 6 (1963), 97–135. MR 0173597 | Zbl 0241.02007
[15] Moisil, Gr. C.: Sur les logiques de Łukasiewicz a un nombre fini de valeurs. Rev. Roum. Math. Pures et Appl. 9 (1964), 905–920. MR 0182557 | Zbl 0149.00401
[16] Moisil, Gr. C.: Essais sur les Logiques non Chrysippiennes. Bucarest, 1972. MR 0398774 | Zbl 0241.02006
[17] Monteiro, A.: Algebras de De Morgan. Lectures given at the Univ. Nac. del Sur, Bahía Blanca, 1962.
[18] Monteiro, A., Varsavsky, O.: Algebras de Heyting monádicas. Actas de las X Jornadas de la Unión Matemática Argentina, Bahía Blanca, 1957, 52–62. (French translation in Notas de Lógica Matemática 1, Instituto de Matemática, Universidad Nacional del Sur, Bahía Blanca 1974, 1–16). MR 1420008
[19] Monteiro, L.: Algebras de Łukasiewicz trivalentes monádicas. Ph. D. Thesis. Notas de Lógica Matemática 32. Univ. Nacional del Sur, Bahía Blanca, 1974. MR 0379184 | Zbl 0298.02063
[20] Sicoe, C.: On many-valued Łukasiewicz algebras. Proc. Japan Acad. 43 (1967), 725–728. MR 0220573 | Zbl 0165.30901
[21] Sicoe, C.: Sur la dèfinition des algèbres Lukasiewicziennes polyvalentes. Rev. Roum. Math. Pures et Appl. 13 (1968), 1027–1030. MR 0233690 | Zbl 0184.01102
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