Mathematical Logic Quarterly 56 (3):228-238 (2010)

Abstract
In this paper we investigate the properties of automorphism groups of countable short recursively saturated models of arithmetic. In particular, we show that Kaye's Theorem concerning the closed normal subgroups of automorphism groups of countable recursively saturated models of arithmetic applies to automorphism groups of countable short recursively saturated models as well. That is, the closed normal subgroups of the automorphism group of a countable short recursively saturated model of PA are exactly the stabilizers of the invariant cuts of the model which are closed under exponentiation. This Galois correspondence is used to show that there are countable short recursively saturated models of arithmetic whose automorphism groups are not isomorphic as topological groups. Moreover, we show that the automorphism groups of countable short arithmetically saturated models of PA are not topologically isomorphic to the automorphism groups of countable short recursively saturated models of PA which are not short arithmetically saturated
Keywords Galois correspondence  models of PA  Short recursive saturation  automorphism groups
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DOI 10.1002/malq.200810050
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References found in this work BETA

Recursively Saturated Nonstandard Models of Arithmetic.C. Smoryński - 1981 - Journal of Symbolic Logic 46 (2):259-286.
Discernible Elements in Models for Peano Arithmetic.Andrzej Ehrenfeucht - 1973 - Journal of Symbolic Logic 38 (2):291-292.
Automorphisms of Models of Arithmetic: A Unified View.Ali Enayat - 2007 - Annals of Pure and Applied Logic 145 (1):16-36.

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