Journal of Mathematical Logic 2 (02):261-296 (2002)

We show that the double jump is definable in the computably enumerable sets. Our main result is as follows: let [Formula: see text] is the Turing degree of a [Formula: see text] set J ≥T0″}. Let [Formula: see text] such that [Formula: see text] is upward closed in [Formula: see text]. Then there is an ℒ property [Formula: see text] such that [Formula: see text] if and only if there is an A where A ≡T F and [Formula: see text]. A corollary of this is that, for all n ≥ 2, the high n computably enumerable degrees are invariant in the computably enumerable sets. Our work resolves Martin's Invariance Conjecture.
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DOI 10.1142/S0219061302000151
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References found in this work BETA

Dynamic Properties of Computably Enumerable Sets.Robert I. Soare - 1996 - In S. B. Cooper, T. A. Slaman & S. S. Wainer (eds.), Computability, Enumerability, Unsolvability: Directions in Recursion Theory. Cambridge University Press. pp. 224--105.
Recursion, Metarecursion, and Inclusion.James C. Owings - 1967 - Journal of Symbolic Logic 32 (2):173-179.
Degrees of Classes of RE Sets.J. R. Shoenfield - 1976 - Journal of Symbolic Logic 41 (3):695-696.

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Degree Invariance in the Π10classes.Rebecca Weber - 2011 - Journal of Symbolic Logic 76 (4):1184-1210.
A Hierarchy of Computably Enumerable Degrees.Rod Downey & Noam Greenberg - 2018 - Bulletin of Symbolic Logic 24 (1):53-89.

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