We are now embarking on what can properly be called model theory. First, let us define some notation in general usage. Consider a theory T, in a language L, which shall be complete unless otherwise stated. We let |T| or |L| denote the cardinality of the language, that is to say, the number of formulas: It is equal to ω if L has finitely or denumerably many relation, function, and constant symbols; it is equal to κ if L has κ > ω of them. If T is complete and has a finite model M, that is its only model up to isomorphism; as this is not a very interesting case, we generally suppose that all the models of T are infinite.
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