Fraïssé limit

Summary

A Fraïssé limit of a class of finitely generated structures is a countable structure that is as symmetric as possible. Its finitely generated substructures are exactly the members of the class, up to isomorphism. Here "as symmetric as possible" means ultrahomogeneous: every isomorphism between finitely generated substructures extends to an automorphism. Fraïssé's theorem gives existence and uniqueness up to isomorphism under four conditions. The class must have the hereditary, joint embedding and amalgamation properties, and only countably many isomorphism types. The rational numbers with their order and the Rado graph are the standard examples.