Set-homogeneous graphs
An infinite relational structure \(M\) is set-homogeneous if, whenever \(U\), \(V\) are finite isomorphic substructures of \(M\), there is an automorphism of \(M\) taking \(U\) to \(V\). This is a weakening of Fraïssé's notion of homogeneity. An example is given of a set-homogeneous graph which is not homogeneous, and the example is characterized by its symmetry properties. A variant of Fraïssé's amalgamation theorem is also given.
scientific article; zbMATH DE number 638648