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Fraïssé's theorem : ウィキペディア英語版
Fraïssé's theorem
In mathematics, Fraïssé's theorem, named after Roland Fraïssé, states that a class ''K'' of finite relational structures is the age of a countable homogeneous relational structure if and only if it satisfies the following four conditions:
* ''K'' is closed under isomorphism;
* ''K'' is closed under taking induced substructures;
* ''K'' has only countably many members up to isomorphism;
* ''K'' has the amalgamation property.
If these conditions hold, then the countable homogeneous structure whose age is ''K'' is unique up to isomorphism.
Fraïssé proved the theorem in the 1950s.
==References==



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