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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. This property plays a crucial role in Fraïssé's theorem which characterises classes of finite structures which arise as ages of countable homogeneous structures. The diagram of the amalgamation property appears in many areas of mathematical logic. Examples include in modal logic as an incestual accessibility relation, and in lambda calculus as a manner of reduction having the Church–Rosser property. ==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: 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 : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Amalgamation property」の詳細全文を読む スポンサード リンク
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