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 ∈ M : (?? ∈ G\H) ?u < b fu = u and J(H) = inf{b ∈ M H} may be invariant, i. e. fixed by all automorphisms of M.