Simplicity of the automorphism groups of generalised metric spaces

Abstract

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

arXiv commentAccepted to Journal of Algebra

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Cited by in corpus (6)

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• Semigroup-valued metric spaces
• Forbidden cycles in metrically homogeneous graphs
• Automorphism groups of homogeneous structures with stationary weak independence relations
• Twenty years of Nešetřil's classification programme of Ramsey classes
• Structural Ramsey Theory and the Extension Property for Partial Automorphisms