Geodesic
Depth, Highness and DNR degrees
Discrete mathematics & theoretical computer science, FCT '15, Tome 19 (2017-2018) no. 4.

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We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of O(1)-deepK, O(1)-deepC , order-deep K and order-deep C sequences. Our main results are that Martin-Loef random sets are not order-deepC , that every many-one degree contains a set which is not O(1)-deepC , that O(1)-deepC sets and order-deepK sets have high or DNR Turing degree and that no K-trival set is O(1)-deepK. 
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     author = {Moser, Philippe and Stephan, Frank},
     title = {Depth, {Highness} and {DNR} degrees},
     journal = {Discrete mathematics & theoretical computer science},
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     number = {4},
     year = {2017-2018},
     doi = {10.23638/DMTCS-19-4-2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-4-2/}
}
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Moser, Philippe; Stephan, Frank. Depth, Highness and DNR degrees. Discrete mathematics & theoretical computer science, FCT '15, Tome 19 (2017-2018) no. 4. doi : 10.23638/DMTCS-19-4-2. http://geodesic.mathdoc.fr/articles/10.23638/DMTCS-19-4-2/

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