Closed Normal Subgroups

Let M be a countable, recursively saturated model of Peano Arithmetic, and let Aut(M) be its automorphism group considered as a topological group with the pointwise stabilizers of finite sets being the basic open subgroups. Kaye proved that the closed normal subgroups are precisely the obvious ones, namely the stabilizers of invariant cuts. A proof of Kaye’s theorem is given here which, although based on his proof, is different enough to yield consequences not obtainable from Kaye’s proof. Mathematics Subject Classification: 03C62, 03H15, 20B27.