Orbits of creative subspaces

Abstract

It is shown that the creative r.e. subspaces fall into infinitely many distinct elementary classes. The techniques also extend to give some new results about orbits of creative subspaces and subfields in L ∗ ( V ∞ ) {L^*}({V_\infty }) and L ∗ ( F ∞ ) {L^*}({F_\infty }) respectively. Finally within each of these new elementary classes we construct infinitely many further orbits in the automorphism group of L ( V ∞ ) L({V_\infty }) .