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Abstract:

The Priestley duality for Wajsberg algebras is developed. The Wajsberg space is a De Morgan space endowed with a family of functions that are obtained in rather natural way. As a first application of this duality, a theorem about unicity of the structure is given. © 1990 Kluwer Academic Publishers.

Registro:

Documento: Artículo
Título:The Priestley duality for Wajsberg algebras
Autor:Martínez, N.G.
Filiación:Departamento de Matemática Facultad de Cs. Exactas y Naturales, U.B.A. Pab. I Ciudad Universitaria, Nuñez-Buenos Aires, 1428, Argentina
Año:1990
Volumen:49
Número:1
Página de inicio:31
Página de fin:46
DOI: http://dx.doi.org/10.1007/BF00401552
Título revista:Studia Logica
Título revista abreviado:Stud Logica
ISSN:00393215
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v49_n1_p31_Martinez

Referencias:

  • Cignoli, R., Proper n-valued Łukasiewicz algebras as S-algebras of Łukasiewicz n-valued propositional calculi (1982) Studia Logica, 41, pp. 3-16
  • R. Cignoli, manuscript; Cornish, W., Fowler, P., Coproducts of De Morgan algebras (1977) Bulletin of the Australian Mathematical Society, 16, pp. 1-13
  • W. Cornish and P. Fowler, Coproducts of Kleene algebras, J. Austral. Math. Soc. Ser A 27, pp. 209–220; Chang, C.C., Algebraic Analysis of many valued logics (1958) Transactions of the American Mathematical Society, 88, pp. 467-490
  • Chang, C.C., A new proof of the completeness of the Łukasiewicz axioms (1959) Transactions of the American Mathematical Society, 93, pp. 74-80
  • Font, J., Rodriguez, A., Torrens, A., Wajsberg algebras (1984) Stochastica, 8 (1), pp. 5-31
  • D. Gluschankof and N. Martinez: The Kleene structure does not determinate the Wajsberg implication. Comunication to the U.M.A. (1987); D. Gluschankof: Doctoral Thesis (in preparation). Fac. Cs. Exactas y Naturales, Universidad de Buenos Aires; R. S. Grigolia: Algebraic analysis of Łukasiewicz-Tarski n-valued logical systems, In Selected Papers on Łukasiewicz Sentential Calculi, Ryszard Wójcicki ed., Warszawa, 1974; Komori, Y., The separation theorem of the X<inf>0</inf>-valued Łukasiewicz propositional logic (1978) Rep. Fac. of Sc., Shizuoka University, 12, pp. 1-5
  • Komori, Y., Super Łukasiewicz implicational logics (1978) Nagoya Math. J., 72, pp. 127-133
  • Komori, Y., Super Łukasiewicz implicational logics (1981) Nagoya Math. J., 84, pp. 119-133
  • A. Monteiro: L'arithmetique des filtres et us espaces topologiques, Notas de Lógica mathemática, Univ. Nac. des Sur. 1974, pp. 29–30; D. Mundici: Interpretation of AF C*-algebras in Łukasiewicz Sentential Calculus, Journal of Functional Analysis, 65, N∘ 1, January 1986; H. A. Priestley: Representation of distributive lattices by means of ordered Stone spaces, Bull. London Math. Soc. 2, pp. 186–190; H. A. Priestley: Ordered topological spaces and the representation of distributive lattices, Proc. London Math. Soc. (3) 24, pp. 507–530; A. J. Rodriguez: Un estudio algebraico de los cálculas proposicionales de Łukasiewicz, Ph. D. Thesis. Universidad de Barcelona, 1980; Torrens, A., W-algebras which are boolean products of members of SR [1] (1987) Studia Logica, 46, pp. 265-275
  • Traczyk, T., On the variety of bounded conmutative BCK-algebras (1979) Math. Jap., 24 (3), pp. 283-292

Citas:

---------- APA ----------
(1990) . The Priestley duality for Wajsberg algebras. Studia Logica, 49(1), 31-46.
http://dx.doi.org/10.1007/BF00401552
---------- CHICAGO ----------
Martínez, N.G. "The Priestley duality for Wajsberg algebras" . Studia Logica 49, no. 1 (1990) : 31-46.
http://dx.doi.org/10.1007/BF00401552
---------- MLA ----------
Martínez, N.G. "The Priestley duality for Wajsberg algebras" . Studia Logica, vol. 49, no. 1, 1990, pp. 31-46.
http://dx.doi.org/10.1007/BF00401552
---------- VANCOUVER ----------
Martínez, N.G. The Priestley duality for Wajsberg algebras. Stud Logica. 1990;49(1):31-46.
http://dx.doi.org/10.1007/BF00401552