# The Complexity of Orbits of Computably Enumerable Sets - Mathematics > Logic

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Abstract: 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 orbitis $\Sigma^1 1$-complete. This result and proof have a number of nicecorollaries: the Scott rank of $\E$ is $\wock +1$; not all orbits areelementarily definable; there is no arithmetic description of all orbits of$\E$; for all finite $\alpha \geq 9$, there is a properly $\Delta^0 \alpha$orbit (from the proof).A few small corrections made in this version

Autor: Peter A. Cholak, Rod Downey, Leo Harrington

Fuente: https://arxiv.org/