ON MAXIMAL-SUBGROUPS OF THE AUTOMORPHISM GROUP OF A COUNTABLE RECURSIVELY SATURATED MODEL OF PA

We show that the stabilizer of an element a of a countable recursively saturated model of arithmetic M is a maximal subgroup of Aut(M) iff the type of a is selective. This is a point of departure for a more detailed study of the relationship between pointwise and setwise stabilizers of certain subsets of M and the types of elements in those subsets. We also show that a complete type of PA is 2-indiscernible iff it is minimal in the sense of Gaifman.