Abstract
This chapter describes the basic semantical and syntactical concepts pertaining to the first-order predicate logic F1, and presents a number of elementary results concerning these concepts. An elementary theory is any theory developed within a first-order predicate logic in which there are no predicate variables, such as the predicate logic F1. The chapter presents a comparison of elementary theories with first-order theories in which predicate variables appear, and second-order theories—or nth-order theories, for n greater than 2 —in which the underlying logic is some second-order, or higher-order, logic. The most important result of a general nature pertaining to the first-order predicate logic is the result that every consistent set of formulas of the first-order predicate logic has a denumerable model, that is, a model with a denumerably infinite domain of individuals. The completeness theorem, together with its corollaries, is important concerning the question of the relations between syntax and semantics.
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