Amalgamation Property
An \emph{amalgam} is a tuple ⟨A,f,B,g,C⟩⟨A,f,B,g,C⟩ such that A,B,CA,B,C are structures of the same signature, and f:A→Bf:A→B, g:A→Cg:A→C are embeddings (injective morphisms).
A class KK of structures is said to have the \emph{amalgamation property} if for every amalgam ⟨A,f,B,g,C⟩⟨A,f,B,g,C⟩ with A,B,C∈KA,B,C∈K and A≠∅A≠∅ there exists a structure D∈KD∈K and embeddings f′:B→D, g′:C→D such that f′∘f=g′∘g.