Depth, Highness and DNR degrees

Philippe Moser; Frank Stephan

doi:10.23638/dmtcs-19-4-2

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arXiv · 1511.05027

Depth, Highness and DNR degrees

Philippe Moser·Frank Stephan

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Abstract

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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Philippe Moser, Frank Stephan. 2015-11-16. Depth, Highness and DNR degrees. https://doi.org/10.23638/dmtcs-19-4-2

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