In the mathematical field of model theory, the amalgamation property is a property of collections of structures that guarantees, under certain conditions, that two structures in the collection can be regarded as substructures of a larger one. 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: A → B, g: A → C are injective morphisms that are referred to as embeddings.

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  • In the mathematical field of model theory, the amalgamation property is a property of collections of structures that guarantees, under certain conditions, that two structures in the collection can be regarded as substructures of a larger one. 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: A → B, g: A → C 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,C ∈ K and A ≠ Ø, there exist both a structure D ∈ K and embeddings f': B → D, g': C → D such that <math>f'\circ f = g' \circ g. </math>
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  • In the mathematical field of model theory, the amalgamation property is a property of collections of structures that guarantees, under certain conditions, that two structures in the collection can be regarded as substructures of a larger one. 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: A → B, g: A → C are injective morphisms that are referred to as embeddings.
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  • Amalgamation property
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