On two questions concerning the automorphism groups of countable recursively saturated models of PA (Q1354336)

The paper is devoted to some problems concerning the automorphism groups of models of Peano arithmetic PA. In particular, it is proved that (1) the automorphism group of a countable recursively saturated model of PA is not divisible and (2) every countably recursively saturated model has a strong initial segment whose setwise stabilizer is not maximal. Definability in structures of the form \((M,I)\), where \(M\) is a model of PA an \(I\) is an initial segment of \(M\), is also considered. A generalization of a result of Kanovej is given.