Limitative theorems of first order classical logic

Abstract

Many of the classic theorems of first order classical logic can be interpreted in two ways, opposed generally. They could be seen like wealth of structures or poverty in the languaje expressive power. The objective of this article is to study three classic theorems of the first order logic: the theorems of compacity, Löwenheim-Skolem and Morley from this last point of view. To interpret this way such theorems does more comprehensible introduction of new concepts and importance of certain metatheorical questions and, in addition, serves to appreciate in all his power one of more important aspects of first order languages. This theorems are localizated in a middle point between an splendid very rich theory and a metatheory that allows to solve, largely, their expresive limitations.