indiscernible sequence?
Morley sequence?
Ramsey theorem?
Erdos-Rado theorem?
Ehrenfeucht-Fraïssé games (back-and-forth games)
Hrushovski construction?
generic predicate?
Galois types are a generalization of types for abstract elementary classes with amalgamation property.
Consider the type (in model theory) $tp(a/M)$ for a first order theory in larger uncountable saturated model $M'$ (of cardinality strictly larger than of the underlying language). By a standard result it can be identified with the orbit of $a$ under the automorphism group $Aut_M(M')$ of $M'$ fixing $M$ pointwise. This is taken as a definition for some infinitary theories in the case we have the monster model. A slightly weaker version can be rephrased in terms of amalgamation.
Let $(K,\lt)$ be an abstract elementary class of structures.
…