The automorphism group of a saturated model has a large dense free subgroup

Abstract

We prove that for a stable theory $T,$ if $M$ is a saturated model of $T$ of cardinality $\lambda$ where $\lambda >\left|T\right|,$ then $Aut(M)$ has a dense free subgroup on $2^{\lambda }$ generators. This affirms a conjecture of Hodges.