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Tent and Ziegler proved that the automorphism group of the Urysohn sphere issimple and that the automorphism group of the Urysohn space is simple modulobounded automorphisms. A key component of their proof is the definition of astationary independence relation (SIR). In this paper we prove that theexistence of a SIR satisfying some extra axioms is enough to prove simplicityof the automorphism group of a countable structure. The extra axioms are chosenwith applications in mind, namely homogeneous structures which admit a"metric-like amalgamation", for example all primitive 3-constrained metricallyhomogeneous graphs of finite diameter from Cherlin's list.

Simplicity of the automorphism groups of generalised metric spaces