Simplicity of the automorphism groups of order and tournament expansions of homogeneous structures
arXiv:1908.05249 · doi:10.1016/j.jalgebra.2021.03.028
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.
The results of the paper now include order expansions as well as expansions to tournaments. Typos corrected. References updated