Amalgamation Property - Definition

Definition

An amalgam can be formally defined as a 5-tuple (A,f,B,g,C) such that A,B,C are structures having the same signature, and f: AB, g: AC are injective morphisms that are referred to as embeddings.

A class K of structures has the amalgamation property if for every amalgam with A,B,CK and A ≠ Ø, there exist both a structure DK and embeddings f': BD, g': CD such that

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