Computably enumerable Turing degrees and the meet property

Durrant, Benedict; Lewis-Pye, Andrew; Meng Ng, Keng; and Riley, James (2016) Computably enumerable Turing degrees and the meet property. Proceedings of the American Mathematical Society, 144 (4). 1735 - 1744. ISSN 0002-9939

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Working in the Turing degree structure, we show that those degrees which contain computably enumerable sets all satisfy the meet property, i.e. if a is c.e. and b < a, then there exists non-zero m < a with b ^m = 0. In fact, more than this is true: m may always be chosen to be a minimal degree. This settles a conjecture of Cooper and Epstein from the 80s.