Abstract
Abstract In the previous chapter, we studied structures independently of the first order language. Nonetheless, if we wish to penetrate the sanctuary of Model Theory, we need a formal language. The language we shall use is a first order language with equality. The objects of such a language are symbols and sequences of symbols. More precisely, we shall have logical symbols, variables, relation symbols, and function symbols. Further to saying which symbols constitute the alphabet of the language, we will have to make explicit which are the allowed combinations of symbols: how one forms the terms and the formulas of the language. The formation rules of such expressions will be of recursive nature, and they will provide us with a decision procedure for checking whether or not a certain sequence of symbols of the alphabet is a formula or a term.
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