Amalgamation Property

A property of a class of structures meaning that any two structures in the class that share a common substructure can be embedded into a single structure from the class in such a way that the two embeddings agree on the common substructure (they are amalgamated).

A class of structures (often a variety or a model class) has the amalgamation property (AP) when any pair of embeddings of a common substructure into two structures can be jointly embedded into a single superstructure so that the two embeddings agree on the common part (there exists an amalgam or pushout for the diagram of embeddings).