The Journal of Symbolic Logic
Department of Mathematics
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; Slaman, Theodore. An Almost Deep Degree. J. Symbolic Logic 66 (2001), no. 2, 881--901. https://projecteuclid.org/euclid.jsl/1183746480
Dartmouth Digital Commons Citation
Cholak, Peter; Groszek, Marcia; and Slaman, Theodore, "An Almost Deep Degree" (2001). Dartmouth Scholarship. 2344.