In model theory, a discipline within the field of mathematical logic, a tame abstract elementary class is an abstract elementary class (AEC) which satisfies a locality property for types called tameness.
Let K be an AEC with joint embedding, amalgamation, and no maximal models.
pointwise (note that types can be defined in a similar manner without using a monster model[2]).
[4] In addition, the following sufficient conditions for a class to be tame are known: Many results in the model theory of (general) AECs assume weak forms of the Generalized continuum hypothesis and rely on sophisticated combinatorial set-theoretic arguments.
[8] On the other hand, the model theory of tame AECs is much easier to develop, as evidenced by the results presented below.