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# ON THE JUMP CLASSES OF NONCUPPABLE ENUMERATION DEGREES

CHARLES M. HARRIS
The Journal of Symbolic Logic
Vol. 76, No. 1 (MARCH 2011), pp. 177-197
Stable URL: http://www.jstor.org/stable/23043323
Page Count: 21
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## Abstract

We prove that for every ${\mathrm{\Sigma }}_{2}^{0}$ enumeration degree b there exists a noncuppable ${\mathrm{\Sigma }}_{2}^{0}$ degree a > 0 e such that b′ ≤ e a′ and a″ ≤ e b″. This allows us to deduce, from results on the high/low jump hierarchy in the local Turing degrees and the jump preserving properties of the standard embedding l: D T → D e , that there exist ${\mathrm{\Sigma }}_{2}^{0}$ noncuppable enumeration degrees at every possible—i.e., above low₁—level of the high/low jump hierarchy in the context of D e .

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