ultrahomogeneous

ultra- +‎ homogeneous

ultrahomogeneous (not comparable)

1. (mathematics) Such that every isomorphism between finitely generated substructures extends to an automorphism of itself.
   • 2016, J. Jonušas, J. D. Mitchell, “Topological 2-generation of automorphism groups of countable ultrahomogeneous graphs”, in arXiv‎:

     We show that if ${\displaystyle \Gamma }$ is ultrahomogeneous, then ${\displaystyle \operatorname {Aut} (\Gamma )}$ has 2-generated dense subgroups, and that under certain conditions given ${\displaystyle f\in \operatorname {Aut} (\Gamma )}$ there exists ${\displaystyle g\in \operatorname {Aut} (\Gamma )}$ such that the subgroup generated by ${\displaystyle f}$ and ${\displaystyle g}$ is dense.