On Splits of Computably enumerable sets
Abstract
Our focus will be on the computably enumerable (c.e.) sets and trivial, non-trivial, Friedberg, and non-Friedberg splits of the c.e. sets. Every non-computable set has a non-trivial Friedberg split. Moreover, this theorem is uniform. V. Yu. Shavrukov recently answered the question which c.e. sets have a non-trivial non-Friedberg splitting and we provide a different proof of his result. We end by showing there is no uniform splitting of all c.e. sets such that all non-computable sets are non-trivially split and, in addition, all sets with a non-trivial non-Friedberg split are split accordingly.
Cite
@article{arxiv.1605.03034,
title = {On Splits of Computably enumerable sets},
author = {Peter Cholak},
journal= {arXiv preprint arXiv:1605.03034},
year = {2016}
}
Comments
Submitted. This version corrects a number of issues raised by the referees. Our thanks to the referees. Learned about another related splitting theorem by Hammond which is now included