Inherent enumerability of strong jump-traceability
Logic
2011-10-10 v1
Abstract
We show that every strongly jump-traceable set obeys every benign cost function. Moreover, we show that every strongly jump-traceable set is computable from a computably enumerable strongly jump-traceable set. This allows us to generalise properties of c.e.\ strongly jump-traceable sets to all such sets. For example, the strongly jump-traceable sets induce an ideal in the Turing degrees; the strongly jump-traceable sets are precisely those that are computable from all superlow Martin-L\"{o}f random sets; the strongly jump-traceable sets are precisely those that are a base for -randomness; and strong jump-traceability is equivalent to strong superlowness.
Keywords
Cite
@article{arxiv.1110.1435,
title = {Inherent enumerability of strong jump-traceability},
author = {David Diamondstone and Noam Greenberg and Daniel Turetsky},
journal= {arXiv preprint arXiv:1110.1435},
year = {2011}
}
Comments
25 pages