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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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Identification Number: 10.1090/proc/12808


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.

Item Type: Article
Official URL:
Additional Information: © 2015 American Mathematical Society
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 23 Feb 2016 09:28
Last Modified: 19 Jun 2024 16:24
Projects: University Research Fellowship
Funders: Royal Society

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