Discrete Mathematics & Theoretical Computer Science (Oct 2017)

Depth, Highness and DNR degrees

  • Philippe Moser,
  • Frank Stephan

DOI
https://doi.org/10.23638/DMTCS-19-4-2
Journal volume & issue
Vol. Vol. 19 no. 4, FCT '15, no. special issue FCT'15

Abstract

Read online

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.

Keywords