A diamond embedding in the computably enumerable quasi degrees

Abstract We investigate the relationship between $$\le _{Q}$$ ≤ Q and $$\le _{T}$$ ≤ T on the computably enumerable sets by asking what kind of lattices can be embedded in the computably enumerable Q degrees, with elements of the lattice in the same Turing degree. We will use a pinball machine to show that the diamond lattice can be embedded in the computably enumerable Q degrees, with all elements of the lattice in the same Turing degree.