Published online by Cambridge University Press: 15 January 2014
The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, ε, such that the question of membership in this orbit is complete. This result and proof have a number of nice corollaries: the Scott rank of ε is
+ 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ε; for all finite α ≥ 9, there is a properly
orbit (from the proof).