Simplicity of the automorphism groups of order and tournament expansions of homogeneous structures

Abstract

We define the notions of a free fusion of structures and a weakly stationary independence relation. We apply these notions to prove simplicity for the automorphism groups of order and tournament expansions of homogeneous structures like the bounded Urysohn space, the random graph, and the random poset.

arXiv commentThe results of the paper now include order expansions as well as expansions to tournaments. Typos corrected. References updated

References in corpus (2)

• On the isometry group of the Urysohn space
• The isometry group of the bounded Urysohn space is simple

Cited by in corpus (5)

• Simplicity of the automorphism groups of generalised metric spaces
• Automorphism groups of homogeneous structures with stationary weak independence relations
• Automorphism groups of linearly ordered homogeneous structures
• Automorphisms of the Rado meet-tree
• Twenty years of Nešetřil's classification programme of Ramsey classes