The Journal of Symbolic Logic
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 ⊕ A is also low. That is. A is “almost deep”. This answers a question of Joekusch. The almost deep degrees form an definable ideal in the r.e. degrees (with jump.)
Cholak, Peter; Groszek, Marcia; and Slaman, Theodore, "An Almost Deep Degree" (2001). Open Dartmouth: Faculty Open Access Articles. 2344.