Measure and cupping in the Turing degrees

Barmpalias, George; and Lewis-Pye, Andrew (2012) Measure and cupping in the Turing degrees. Proceedings of the American Mathematical Society, 140 (10). pp. 3607-3622. ISSN 0002-9939
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We answer a question of Jockusch by showing that the measure of the Turing degrees that 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.

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