PERMUTATIONS AND PRESENTATIONS

We say that an automorphism Phi of E (the lattice of recursively enum erable sets module the finite sets) is induced by a permutation p iff for all e, Phi(W-e) = p(W-e). A permutation h is called a presentatio n of Phi iff for all e, Phi(W-e) = W-h(e). In this paper, we will exp lore the degree-theoretic connections between these two notions. Using a new proof of the well-known fact that every automorphism is induced by a permutation p, we show that such a p can be found recursively in h + circle divide'', where h is a presentation of Phi. The main resul t of the paper is to show that there is an effective automorphism of E which is not induced by a Delta(2)-permutation.