Full Satisfaction Classes, Definability, and Automorphisms

We show that for every countable recursively saturated model M of Peano arithmetic and subset A⊆M, there exists a full satisfaction class SA⊆M2 such A is definable in (M,SA) without parameters. It follows model, which makes element definable, thus the expanded minimal rigid. On other hand, as observed by Roman Kossak, S are two elements have same arithmetical type, but exactly one them S. In particular, automorphism group with never equal to original model. The analogue first result proved here classes was obtained also Kossak partial inductive classes. However, proof relied on induction scheme crucial way, so recapturing setting requires quite different arguments.