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A join theorem for the computably enumerable degrees |
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| Authors: | Carl G. Jockusch Jr. Angsheng Li Yue Yang |
| Affiliation: | Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801 ; Institute of Software, Chinese Academy of Sciences, P. O. Box 8718, Beijing, 100080, People's Republic of China ; Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260 |
| Abstract: | It is shown that for any computably enumerable (c.e.) degree  , if  , then there is a c.e. degree  such that  (so  is low and  is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low c.e. degrees are not elementarily equivalent as partial orderings. |
| Keywords: | Join theorem computably enumerable degree definable ideals Turing jump |
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