I've been learning about countable ultrahomogeneous structures, where ultrahomogeneous means every isomorphism of finitely generated substructures extends to an automorphism of the whole structure. For instance, $(\mathbb{Q},<)$ is the unique countable ultrahomogeneous linear order.

For linear orders, it is nice to have an easy to understand instantiation of the ultrahomogeneous structure instead of an amorphous highly-uniform linear order. In trying to understand the countable ultrahomogenous graphs and boolean algebras, I was hoping to find some good constructions to help see what these are like, rather than a random/generic structure or a universal one (like being a Fraisse Limit of a class of finite structures).

So, anything to help me get a grasp of these (or other) ultrahomogeneous structures would be appreciated.


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