Finite cupping sets

We show that given any (Turing) degree 0<c≤0’ and any uniformly Δ2 sequence of degrees b 0 ,b 1 ,b 2 ,.. such that ∀i(b i ≱ c), there exists 0<a<0’ such that for all i≥0, a∨b i ≱ c. If c is c.e. and b 0 ,b 1 ,b 2 ,.. are uniformly (strictly) below c then there exists such an a below c.