Completeness of first order logic
María Manzano · Model Theory · 1999
Abstract In the previous chapter we saw that in order to speak of a structure or a class of structures it is convenient to introduce a formal language appropriate to each case. Among the formulas of the language, we shall usually be interested in determining which ones are true in the structure (or class of structures), and even though we rely on the semantic notion of truth, it is often difficult to establish the truth of a formula by recourse solely to the direct verification of the truth conditions. Much more difficult, however, is to determine if a formula is a consequence of a set of formulas.