In this chapter we present the syntax and semantics of classical first-order logic. We also state and prove a Model Existence Theorem, essentially a semantical result, asserting the existence of certain models. We use the theorem to establish some basic facts about first-order logic, suck as compactness and Löwenheim-Skolem results. In the next chapter we introduce proof procedures for first-order logic, and then the Model Existence Theorem will find its primary application, in proving completeness. Further consequences will be found in Chapter 8, after we have considered the implementation of proof procedures. This section sets forth the syntax of first-order logic, which is a considerably more complicated business than it was in the propositional case.
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