Generics in invariant subsets of the group of order preserving permutations of Q

Abstract

Let $\rho \in \mathrm{Aut}(Q,<)$ and $C_{\rho }$ be the closure of the conjugacy class of ρ in $\mathrm{Aut}(Q,<)$. We show that $C_{\rho }$ contains a conjugacy class, say C, which is comeagre in $C_{\rho }$. We describe representatives of C. Furthermore, we show that the family of finite partial maps extendable to elements of C has the cofinal amalgamation property.