Model theory of the computably enumerable many-one degrees
André Nies · Logic Journal of IGPL · 2000
We investigate model theoretic properties of Rm, the partial order of computably enumerable many-one degrees. We prove that all nontrivial final segments and the set of minimal degrees are automorphism bases, and that some proper half open initial segment is an elementary substructures of Rm - {1}. This shows that Rm is not a minimal model. In an appendix, we show that the many-one degree of an r-maximal set is join irreducible.