Simplicity of the automorphism groups of generalised metric spaces

[摘要] 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Homogeneous structures;Automorphism groups;Independence relations;Generalised metric spaces