A commutative diagram of the amalgamation property.
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.
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In the mathematical field of model theory, the amalgamationproperty is a property of collections of structures that guarantees, under certain conditions...
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A similar but different notion to the joint embedding property is the amalgamationproperty. To see the difference, first consider the class K (or simply...
classes, it is hereditary, it is joint-embedded, and it holds the amalgamationproperty.: p.3 5 is the value of the central cell of the first non-trivial...
model-complete theory, whose theory of universal consequences has the amalgamationproperty, has quantifier elimination. The models of the theory of the universal...
conditions are equivalent: T* is a model completion of T T has the amalgamationproperty. If T also has universal axiomatization, both of the above are also...
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/3\mathbf {Z} ).} The more general construction of free product with amalgamation is correspondingly a special kind of pushout in the same category. Suppose...
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The pair ( C , ≤ ) {\displaystyle (\mathbf {C} ,\leq )} has the amalgamationproperty if A ≤ B 1 , B 2 {\displaystyle A\leq B_{1},B_{2}} then there is...
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categoricity conjecture) for Abstract Elementary Classes with the amalgamationproperty, that are tame. In another work with VanDieren, they also initiated...
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acids, thus dissolving them. Its hydrogen bonding causes its many unique properties, such as having a solid form less dense than its liquid form, a relatively...
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However, as Ivor Grattan-Guinness has discovered, this is in fact an amalgamation by Cantor's editor, Ernst Zermelo, of two letters from Cantor to Dedekind...
operator. Revenue is also generated from managing and leasing commercial property. As of 2017[update], the company had 62 hotels and resorts around the world...
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