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Abstract:

It is shown that in a linearly ordered MV-algebra A, the implication is unique if and only if the identity function is the unique De Morgan automorphism on A. Modulo categorical equivalence, our uniqueness criterion recalls Ohkuma's rigidness condition for totally ordered abelian groups. We also show that, if A is an Archimedean totally ordered MV-algebra, then each non-trivial De Morgan automorphism of the underlying involutive lattice of A yields a new implication on A, which is not isomorphic to the original implication. © 2001 Elsevier Science B.V.

Registro:

Documento: Artículo
Título:Uniqueness of the implication for totally ordered MV-algebras
Autor:Martínez, N.G.; Petrovich, A.
Filiación:Departamento de Matematica, Facultad de Ciencias Exactas, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:03G25; 06D05; 06E15; De Morgan algebras; MV-algebras; Priestley's duality; Rigidness
Año:2001
Volumen:108
Número:1-3
Página de inicio:261
Página de fin:268
DOI: http://dx.doi.org/10.1016/S0168-0072(00)00050-6
Título revista:Annals of Pure and Applied Logic
Título revista abreviado:Ann. Pure Appl. Logic
ISSN:01680072
CODEN:APALD
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_01680072_v108_n1-3_p261_Martinez

Referencias:

  • Cignoli, R., D'Ottaviano, I., Mundici, D., (1994) Algebras Das Lógicas de Lukasiewicz, 12. , Centro de Lógica, Epistemologia e História da Ciencia-Unicamp
  • Conrad, P., Darnel, M., Lattice-ordered groups whose lattices determine their additions (1992) Trans. Amer. Math. Soc., 30 (2), pp. 577-598
  • Cornish, W., Fowler, P., Coproducts of De Morgan algebras (1977) Bull. Austral. Math. Soc., 16, pp. 1-13
  • Chang, C.C., Algebraic analysis of many-valued logics (1958) Trans. Amer. Math. Soc., 88, pp. 467-490
  • Martínez, N., Priestley, H.A., Uniqueness of the implication in MV-algebras (1995) Mathware J., 11 (3), pp. 229-245
  • Mundici, D., Interpretation of AF-C* algebras in Lukasiewicz sentential Calculus (1986) J. Funct. Anal., 65 (1), pp. 15-63
  • Ohkuma, T., Sur quelques ensembles ordonnés linéairment (1954) Fund. Math., 43, pp. 326-337

Citas:

---------- APA ----------
Martínez, N.G. & Petrovich, A. (2001) . Uniqueness of the implication for totally ordered MV-algebras. Annals of Pure and Applied Logic, 108(1-3), 261-268.
http://dx.doi.org/10.1016/S0168-0072(00)00050-6
---------- CHICAGO ----------
Martínez, N.G., Petrovich, A. "Uniqueness of the implication for totally ordered MV-algebras" . Annals of Pure and Applied Logic 108, no. 1-3 (2001) : 261-268.
http://dx.doi.org/10.1016/S0168-0072(00)00050-6
---------- MLA ----------
Martínez, N.G., Petrovich, A. "Uniqueness of the implication for totally ordered MV-algebras" . Annals of Pure and Applied Logic, vol. 108, no. 1-3, 2001, pp. 261-268.
http://dx.doi.org/10.1016/S0168-0072(00)00050-6
---------- VANCOUVER ----------
Martínez, N.G., Petrovich, A. Uniqueness of the implication for totally ordered MV-algebras. Ann. Pure Appl. Logic. 2001;108(1-3):261-268.
http://dx.doi.org/10.1016/S0168-0072(00)00050-6