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Abstract:

It is shown that axiomatic extensions of intuitionistic propositional calculus defining univocally new connectives, including those proposed by Gabbay, are strongly complete with respect to valuations in Heyting algebras with additional operations. In all cases, the double negation of such a connective is equivalent to a formula of intuitionistic calculus. Thus, under the excluded third law it collapses to a classical formula, showing that this condition in Gabbay's definition is redundant. Moreover, such connectives can not be interpreted in all Heyting algebras, unless they are already equivalent to a formula of intuitionistic calculus. These facts relativize to connectives over intermediate logics. In particular, the intermediate logic with values in the chain of length n may be "completed" conservatively by adding a single unary connective, so that the expanded system does not allow further axiomatic extensions by new connectives.

Registro:

Documento: Artículo
Título:An algebraic approach to intuitionistic connectives
Autor:Caicedo, X.; Cignoli, R.
Filiación:Departamento de Matemáticas, Universidad de Los Andes, Apartado Aéreo 4976, Bogotá, D.C., Colombia
Departamento de Matemáticas, Fac. de Ciencias Exactas y Naturales, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Año:2001
Volumen:66
Número:4
Página de inicio:1620
Página de fin:1636
DOI: http://dx.doi.org/10.2307/2694965
Título revista:Journal of Symbolic Logic
Título revista abreviado:J. Symb. Logic
ISSN:00224812
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00224812_v66_n4_p1620_Caicedo

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Citas:

---------- APA ----------
Caicedo, X. & Cignoli, R. (2001) . An algebraic approach to intuitionistic connectives. Journal of Symbolic Logic, 66(4), 1620-1636.
http://dx.doi.org/10.2307/2694965
---------- CHICAGO ----------
Caicedo, X., Cignoli, R. "An algebraic approach to intuitionistic connectives" . Journal of Symbolic Logic 66, no. 4 (2001) : 1620-1636.
http://dx.doi.org/10.2307/2694965
---------- MLA ----------
Caicedo, X., Cignoli, R. "An algebraic approach to intuitionistic connectives" . Journal of Symbolic Logic, vol. 66, no. 4, 2001, pp. 1620-1636.
http://dx.doi.org/10.2307/2694965
---------- VANCOUVER ----------
Caicedo, X., Cignoli, R. An algebraic approach to intuitionistic connectives. J. Symb. Logic. 2001;66(4):1620-1636.
http://dx.doi.org/10.2307/2694965