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 M 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, Omega subset of M is a very good interstice, and a is an element of Omega, then the stabilizer of a is a maximal subgroup of Aut(M) if and only if the type of a is selective and rational. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim