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Abstract:

The infinite-valued logic of Łukasiewicz was originally defined by means of an infinite-valued matrix. Łukasiewicz took special forms of negation and implication as basic connectives and proposed an axiom system that he conjectured would be sufficient to derive the valid formulas of the logic; this was eventually verified by M. Wajsberg. The algebraic counterparts of this logic have become know as Wajsberg algebras. In this paper we show that a Wajsberg algebra is complete and atomic (as a lattice) if and only if it is a direct product of finite Wajsberg chains. The classical characterization of complete and atomic Boolean algebras as fields of sets is a particular case of this result. © 1991 Polish Academy of Sciences.

Registro:

Documento: Artículo
Título:Complete and atomic algebras of the infinite valued Łukasiewicz logic
Autor:Cignoli, R.
Filiación:Departamento de Matemática facultad de ciencias exactas y naturales, Ciudad Universitaria, Buenos Aires, 1428, Argentina
Año:1991
Volumen:50
Número:3-4
Página de inicio:375
Página de fin:384
DOI: http://dx.doi.org/10.1007/BF00370678
Título revista:Studia Logica
Título revista abreviado:Stud Logica
ISSN:00393215
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00393215_v50_n3-4_p375_Cignoli

Referencias:

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Citas:

---------- APA ----------
(1991) . Complete and atomic algebras of the infinite valued Łukasiewicz logic. Studia Logica, 50(3-4), 375-384.
http://dx.doi.org/10.1007/BF00370678
---------- CHICAGO ----------
Cignoli, R. "Complete and atomic algebras of the infinite valued Łukasiewicz logic" . Studia Logica 50, no. 3-4 (1991) : 375-384.
http://dx.doi.org/10.1007/BF00370678
---------- MLA ----------
Cignoli, R. "Complete and atomic algebras of the infinite valued Łukasiewicz logic" . Studia Logica, vol. 50, no. 3-4, 1991, pp. 375-384.
http://dx.doi.org/10.1007/BF00370678
---------- VANCOUVER ----------
Cignoli, R. Complete and atomic algebras of the infinite valued Łukasiewicz logic. Stud Logica. 1991;50(3-4):375-384.
http://dx.doi.org/10.1007/BF00370678