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 that 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,[clarification needed] and in lambda calculus as a manner of reduction having the Church–Rosser property.