An almost deep degree

Journal of Symbolic Logic 66 (2):881-901 (2001)

Abstract
We show there is a non-recursive r.e. set A such that if W is any low r.e. set, then the join W $\oplus$ A is also low. That is, A is "almost deep". This answers a question of Jockusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.)
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DOI 10.2307/2695051
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