An almost deep degree
Peter A. Cholak, Marcia J. Groszek, Theodore A. Slaman · Journal of Symbolic Logic · 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 ⊕ 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.)