Fraïssé's theorem
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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.[1]
Fraïssé proved the theorem in the 1950s.
For a proof and more details see Section 1.2 and Appendix A of this thesis.
References
- ↑ Meenaxi Bhattacharjee; Dugald Macpherson; Rögnvaldur G. Möller; Peter M. Neumann. Notes on Infinite Permutation Groups. Lecture Notes in Mathematics. 1689. 1998: Springer. pp. 155–158. ISBN 978-3-540-64965-6.
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