Crítica, Revista Hispanoamericana de Filosofía, Volume 35, number 103, abril 2003
A Structural Characterization of Extended Correctness-Completeness in Classical Logic
[Una caracterización estructural de la correctud-completud extendida en la lógica clásica]
José Alfredo Amor
Facultad de Ciencias
Universidad Nacional Autónoma de México

Abstract: In this paper I deal with first order logic and axiomatic systems. I present the metalogical results that show the property of satisfying Modus Ponens as a necessary and sufficient condition for the extended completeness of the system, and to the Deduction Metatheorem as a necessary and sufficient condition for the extended correctness of the system. Both supposing that the system satisfies the corresponding restricted properties. These results show that the choice of that rule of inference and of that metatheorem, for any particular axiomatic system, are not a matter of personal liking or of practical convenience, but they play a fundamental role for the extended correctness-completeness properties of the axiomatic system. As a matter of fact, they can be considered as structural properties that characterize the fulfilling of the Extended Correctness and Completeness theorem for the axiomatic system.
Keywords: logical consequence, axiomatic system, compactness, semantics

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