On n-Tardy Sets
Logic
2011-01-04 v1
Abstract
Harrington and Soare introduced the notion of an n-tardy set. They showed that there is a nonempty property Q(A) such that if Q(A) then A is 2-tardy. Since they also showed no 2-tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete. Our study of n-tardy sets takes off from where Harrington and Soare left off. We answer all the open questions asked by Harrington and Soare about n-tardy sets. We show there is a 3-tardy set A that is not computed by any 2-tardy set B. We also show that there are nonempty properties such that if then A is properly n-tardy.
Cite
@article{arxiv.1101.0228,
title = {On n-Tardy Sets},
author = {Peter A. Cholak and Peter M. Gerdes and Karen Lange},
journal= {arXiv preprint arXiv:1101.0228},
year = {2011}
}