Amalgamation property

Summary

A class of structures has the amalgamation property when any two members that share a common part fit together in a third member. In the third member, the two copies of the common part must coincide. It is one of the three conditions in Fraïssé's theorem, which builds a countable homogeneous structure, the Fraïssé limit, from a class of finite structures. It also appears in algebra, for example in the study of amalgamated free products of groups.