 By the extended completeness theorem, these two approaches
| give basically the same results about consequences of T.
| However, owing to the fact that models of T also have
| non-first-order properties, such as isomorphism,
| submodels, extensions, plus many others, the
| second approach leads to the field now
| known as model theory.
|
| We shall give in the rest of this section some examples of theories
| and their models to show the intimate connections that model theory
| has with other branches of ma