Strong amalgamation property

Definition

An amalgam is a tuple (A,f,B,g,C) such that A,B,C are structures of the same signature, and f : A → B, g : A → C are embeddings (injective morphisms).

A class K of structures is said to have the strong amalgamation property, or SAP for short, if for every amalgam with A,B,C ∈ K and A ≠ Ø there exists a structure D ∈ K and embeddings f ' : B → D, g' : C → D such that f 'of = g'og and Im(f ')∩Im(g') = Ø, where Im(f ') = {f '(x) | x ∈ B}.

Properties that imply the SAP

Properties implied by the SAP

[Generate list of all classes that mention the strong amalgamation property together with it's value in that class (under construction)].