We give a general criterion for the (bounded) simplicity of the automorphism groups of certain countable structures and apply it to show that the isometry group of the Urysohn space modulo the normal subgroup of bounded isometries is a simple group.
we show that the automorphism groups of certain countable structures obtained using the Hrushovski amalgamation method are simple groups. The structures we consider are the 'uncollapsed' structures of infinite Morley rank obtained by the ab initio construction and the (unstable) ℵ 0-categorical pseudoplanes. The simplicity of the automorphism groups of… (More)
We give a uniform construction of free pseudospaces of dimension n extending work in . 3 This yields examples of-stable theories which are n-ample, but not n + 1-ample. The prime models of 4 these theories are buildings associated to certain right-angled Coxeter groups. 5 §1. Introduction. In the investigation of geometries on strongly minimal sets the 6… (More)
We prove that the generic type of a non-cyclic torsion-free hyperbolic group G is foreign to any interpretable abelian group, hence also to any interpretable field. This result depends, among other things, on the definable simplicity of a non-cyclic torsion-free hyperbolic group, and we take the opportunity to give a proof of the latter using Sela's… (More)
If Γ is a 2-Moufang generalized n-gon for n ≤ 6, then Γ is Moufang.