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  1. The complexity of orbits of computably enumerable sets.Peter A. Cholak, Rodney Downey & Leo A. Harrington - 2008 - Bulletin of Symbolic Logic 14 (1):69 - 87.
    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 ${\Sigma _1^1 }$ -complete. This result and proof have a number of nice corollaries: the Scott rank of ε is $\omega _1^{{\rm{CK}}}$ + 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 $\Delta (...)
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