ry is as follows:  Let $A$ be a model for $L$;
| then the 'theory of' $A$ is the set of all sentences which
| hold in $A$.  The theory of any model $A$ is obviously
| a complete theory.
|
| Historically, the importance of theories stems from the following
| two facts.  Once the axioms of a theory are given, then by using
| the relation |- we can find out, in a syntactical manner, all the
| consequences of T.  On the other hand, by using the satisfaction
| relation, we can also study all the models of T.
|
|