Fraïssé limit
In mathematical logic, specifically in the discipline of model theory, the Fraïssé limit (also called the Fraïssé construction or Fraïssé amalgamation) is a method used to construct (infinite) mathematical structures from their (finite) substructures. It is a special example of the more general concept of a direct limit in a category. The technique was developed in the 1950s by its namesake, French logician Roland Fraïssé.

The main point of Fraïssé's construction is to show how one can approximate a (countable) structure by its finitely generated substructures. Given a class formula_1 of finite relational structures, if formula_1 satisfies certain properties (described below), then there exists a unique countable structure formula_3, called the Fraïssé limit of formula_1, which contains all the elements of formula_1 as substructures.

The general study of Fraïssé limits and related notions is sometimes called Fraïssé theory. This field has seen wide applications to other parts of mathematics, including topological dynamics, functional analysis, and Ramsey theory.
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mathematical logic
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model theory
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mathematical structures
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substructures
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direct limit
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Roland Fraïssé
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relational structures
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topological dynamics
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functional analysis
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Ramsey theory
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Fraïssé limit
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Fraïssé limit
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Fraïssé limit
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