Structural properties and Σ20 enumeration degrees
André Nies, Andrea Sorbi · Journal of Symbolic Logic · 2000
Abstract We prove that each Σ20 set which is hypersimple relative to ∅′ is noncuppable in the structure of the Σ20 enumeration degrees. This gives a connection between properties of Σ20 sets under inclusion and and the Σ20 enumeration degrees. We also prove that some low non-computably enumerable enumeration degree contains no set which is simple relative to ∅′.