In many areas of mathematics (like partial orderings, groups, or graphs), we write down some axioms and immediately have several different models of these axioms in mind. In the setting of first-order logic, this corresponds to writing down a set Σ of sentences in a language and looking at the elementary class Mod(∑). Since Mod(Σ)=Mod(Cn(Σ)) by Proposition 6.5.3, and Cn(Σ) is a theory by Proposition 6.5.4, we can view this situation as looking at the (elementary) class of models of a theory.
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