Fraisse's Theorem, developed in the 1950s by the French logician Roland Fraisse, shows that for a class of finite relational structures satisfying certain closure and amalgamation properties, there exists a unique countable structure, called the Fraisse limit of that class, which contains every structure in the class as a substructure and can be approximated arbitrarily well by those finite substructures. The construction is a special case of a direct limit taken in a category, and the resulting theory of Fraisse limits has found wide application beyond model theory itself, including in topological dynamics, functional analysis, and Ramsey theory.
Facts
StatementFor a Fraisse class K of finite structures, there is a unique (up to isomorphism), countable, homogeneous structure Flim(K) whose age is exactly K. 2 Classification
Statement Form Sources
1. Wikipedia: Fraïssé limit
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Given a class K } of finite relational structures, if K } satisfies certain properties (described below), then there exists a unique countable structure Flim ( K ) (\mathbf {K} )} , called the Fraïssé limit of K } , which contains all the elements of K } as substructures.
2. Fraisse limit (Wikipedia)
Fraisse's theorem sectionQuote, Fraisse's theorem section
there is a unique (up to isomorphism), countable, homogeneous structure
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