Interstitial and pseudo gaps in models of Peano Arithmetic

In this paper we study the automorphism groups of models of Peano Arithmetic. Kossak, Kotlarski, and Schmerl [9] shows that the stabilizer of an unbounded element a of a countable recursively saturated model of Peano Arithmetic a is a maximal subgroup of Aut(M) if and only if the type of a is selective. We extend this result by showing that if M is a countable arithmetically saturated model of Peano Arithmetic, Ω ⊂ M is a very good interstice, and a ∈ Ω, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational.