AUTOMORPHISMS OF COUNTABLE RECURSIVELY SATURATED MODELS OF PA - OPEN SUBGROUPS AND INVARIANT CUTS

Let M be a countable recursively saturated model of PA and H an open subgroup of G = Aut(M). We prove that I(H) = sup{b is an element of M : (There Exists f is an element of G\H)(For All u < b) fu = u} and J(H) = inf{b is an element of M : G(b) subset of or equal to H} may be invariant, i.e. fixed by all automorphisms of M.