The Complexity of Orbits of Computably Enumerable Sets

The goal of this paper is to announce there is a single orbit of the c.e. sets with inclusion, E, such that the question of membership in this orbit is 1 1-complete. This result and proof have a number of nice corollaries: the Scott rank of E is CK 1 + 1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of E; for all finite 9, there is a properly 0 orbit (from the proof).

• Type: Journal
• Year: 2008
• Where: BSL
• Authors: Peter Cholak, Rodney G. Downey, Leo Harrington
• Keywords: BSL 2008, Nice Corollaries, Orbit, Single Orbit