THE COMPLEXITY OF ORBITS OF COMPUTABLY ENUMERABLE SETS

THE COMPLEXITY OF ORBITS OF COMPUTABLY ENUMERABLE SETS

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by Peter A. Cholak , Rodney Downey , Leo , A. Harrington

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@MISC{Cholak_thecomplexity,
    author = {Peter A. Cholak and Rodney Downey and Leo and A. Harrington},
    title = {THE COMPLEXITY OF ORBITS OF COMPUTABLY ENUMERABLE SETS},
    year = {}
}

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Abstract

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 orbit is Σ1 1-complete. This result and proof have a number of nice corollaries: the Scott rank of E is ωCK 1 + 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 ∆0 α orbit (from the proof). 1.

Citations

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