Computably enumerable Turing degrees and the meet property
Durrant, B., Lewis-Pye, A., Meng Ng, K. & Riley, J.
(2016).
Computably enumerable Turing degrees and the meet property.
Proceedings of the American Mathematical Society,
144(4), 1735 - 1744.
https://doi.org/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 |
|---|---|
| Copyright holders | © 2015 American Mathematical Society |
| Departments | LSE > Academic Departments > Mathematics |
| DOI | 10.1090/proc/12808 |
| Date Deposited | 23 Feb 2016 |
| URI | https://researchonline.lse.ac.uk/id/eprint/65480 |
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- http://www.lse.ac.uk/Mathematics/people/Andrew-Lewis-Pye.aspx (Author)
- http://www.ams.org/journals/proc/2016-144-04/S0002-9939-2015-12808-0/home.html (Publisher)
- https://www.scopus.com/pages/publications/84955477020 (Scopus publication)
- http://www.ams.org/journals/proc/ (Official URL)