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 $λ$ where $λ> \big|T\big|,$ then $Aut(M)$ has a dense free subgroup on $2^λ$ generators. This affirms a conjecture of Hodges.