We prove the following three theorems on the enumeration degrees of Sigma(2)(0) sets. Theorem A: There exists a nonzero noncuppable Sigma(2)(0) enumeration degree, Theorem B: Every nonzero Delta(2)(0) enumeration degree is cuppable to 0(3)', by an incomplete total enumeration degree. Theorem C: There exists a nonzero low Delta(2)(0) enumeration degree with the anticupping property.
Cooper, S.B., Sorbi, A., Yi, X. (1996). Cupping and noncupping in the enumeration degrees of Σ02 sets. ANNALS OF PURE AND APPLIED LOGIC, 82(3), 317-342 [10.1016/S0168-0072(96)00009-7].
Cupping and noncupping in the enumeration degrees of Σ02 sets
Sorbi A.;
1996-01-01
Abstract
We prove the following three theorems on the enumeration degrees of Sigma(2)(0) sets. Theorem A: There exists a nonzero noncuppable Sigma(2)(0) enumeration degree, Theorem B: Every nonzero Delta(2)(0) enumeration degree is cuppable to 0(3)', by an incomplete total enumeration degree. Theorem C: There exists a nonzero low Delta(2)(0) enumeration degree with the anticupping property.
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https://hdl.handle.net/11365/1082610