AUTOMORPHISMS OF RECURSIVELY SATURATED MODELS OF ARITHMETIC

We give an examination of the automorphism group Aut(M) 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(M1) is-not-equal-approximately-equal-to Aut(M2), as topological groups with a natural topology. Other results include a classification of the normal subgroups of Aut(M) of the form {g: g t A half arrow pointing up and to the right = id(A)}, for sets A subset-or-equal-to M, and a highly homogeneous representation of Aut(M) as a subgroup of Aut(Q, <).