The degrees below a 1-generic degree $

Journal of Symbolic Logic 51 (3):770 - 777 (1986)
Abstract
It is shown that the nonrecursive predecessors of a 1-generic degree $ are all 1-generic. As a corollary, it is shown that the 1-generic degrees are not densely ordered
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Rod Downey & Liang Yu (2006). Arithmetical Sacks Forcing. Archive for Mathematical Logic 45 (6):715-720.
Rutger Kuyper (2013). Natural Factors of the Muchnik Lattice Capturing IPC. Annals of Pure and Applied Logic 164 (10):1025-1036.
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