Fraïssé's theorem

In mathematics, Fraïssé's theorem, named after Roland Fraïssé, states that a class K of finite relational structures is the age of a countable homogeneous relational structure if and only if it satisfies the following four conditions:

If these conditions hold, then the countable homogeneous structure whose age is K is unique up to isomorphism.

Fraïssé proved the theorem in the 1950s.