We prove that each Σ_2~0 set which is hypersimple relative to φ' is noncuppable in the structure of the Σ_2~0 enumeration degrees. This gives a connection between properties of Σ_2~0 sets under inclusion and and the Σ_2~0 enumeration degrees. We also prove that some low non-computably enumerable enumeration degree contains no set which is simpler relative to φ'.
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