Automorphisms of recursively saturated models of arithmetic

Annals of Pure and Applied Logic 55 (1):67-99 (1991)
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We give an examination of the automorphism group Aut of a countable recursively saturated model M of PA. The main result is a characterisation of strong elementary initial segments of M as the initial segments consisting of fixed points of automorphisms of M. As a corollary we prove that, for any consistent completion T of PA, there are recursively saturated countable models M1, M2 of T, such that Aut[ncong]Aut, as topological groups with a natural topology. Other results include a classification of the normal subgroups of Aut of the form [lcub]g: g [uharr] A = idA[rcub], for sets A M, and a highly homogeneous representation of Aut as a subgroup of Aut



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Roman Kossak
City University of New York

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Models and types of Peano's arithmetic.Haim Gaifman - 1976 - Annals of Mathematical Logic 9 (3):223-306.
Models of Peano Arithmetic.Richard Kaye - 1991 - Clarendon Press.
Toward model theory through recursive saturation.John Stewart Schlipf - 1978 - Journal of Symbolic Logic 43 (2):183-206.
Recursively saturated nonstandard models of arithmetic.C. Smoryński - 1981 - Journal of Symbolic Logic 46 (2):259-286.

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