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 Σ11-complete. This result and proof have a number of nice corollaries: the Scott rank of ℰ is ω1CK+1; not all orbits are elementarily definable; there is no arithmetic description of all orbits of ℰ; for all finite α ≥ 9, there is a properly Δ0α orbit (from the proof).
Permanent link to this document: http://projecteuclid.org/euclid.bsl/1208358844
Digital Object Identifier: doi:10.2178/bsl/1208358844
Mathematical Reviews number (MathSciNet): MR2395047
Zentralblatt MATH identifier: 1142.03022