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.
Read more about Amalgamation Property: Definition, Examples, Strong Amalgamation Property
Famous quotes containing the word property:
“The charming landscape which I saw this morning is indubitably made up of some twenty or thirty farms. Miller owns this field, Locke that, and Manning the woodland beyond. But none of them owns the landscape. There is property in the horizon which no man has but he whose eye can integrate all parts, that is, the poet. This is the best part of these men’s farms, yet to this their warranty-deeds give no title.”
—Ralph Waldo Emerson (1803–1882)