Measure and cupping in the Turing degrees
George Barmpalias, Andrew E.M. Lewis

Abstract:
We answer a question of Jockusch by showing that the measure of the
Turing degrees which satisfy the cupping property is 0. In fact, every
2-random degree has a strong minimal cover, and so fails to satisfy
the cupping property.

Keywords: Measure, Turing degrees, cupping, strong minimal cover, randomness