We prove that every Turing degree a bounding some non-GL₂ degree is recursively enumerable in and above (r.e.a.) some 1-generic degree.
Klaus Ambos-Spies. Decheng Ding. Wei Wang. Liang Yu. "Bounding non-GL₂ and R.E.A.." J. Symbolic Logic 74 (3) 989 - 1000, September 2009. https://doi.org/10.2178/jsl/1245158095