Annals of Pure and Applied Logic 138 (1):211-219 (2006)

Abstract
Say a set Gω is 1-generic if for any eω, there is a string σG such that {e}σ↓ or τσ↑). It is known that can be split into two 1-generic degrees. In this paper, we generalize this and prove that any nonzero computably enumerable degree can be split into two 1-generic degrees. As a corollary, no two computably enumerable degrees bound the same class of 1-generic degrees
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DOI 10.1016/j.apal.2005.06.012
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References found in this work BETA

Double Jumps of Minimal Degrees.Carl G. Jockusch & David B. Posner - 1978 - Journal of Symbolic Logic 43 (4):715 - 724.
Minimal Degrees and the Jump Operator.S. B. Cooper - 1973 - Journal of Symbolic Logic 38 (2):249-271.
Minimal Degrees Recursive in 1-Generic Degrees.C. T. Chong & R. G. Downey - 1990 - Annals of Pure and Applied Logic 48 (3):215-225.
The Degrees Below a 1-Generic Degree $.Christine Ann Haught - 1986 - Journal of Symbolic Logic 51 (3):770 - 777.

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