Computably enumerable partial orders
Logic
2011-10-19 v1
Abstract
We study the degree spectra and reverse-mathematical applications of computably enumerable and co-computably enumerable partial orders. We formulate versions of the chain/antichain principle and ascending/descending sequence principle for such orders, and show that the former is strictly stronger than the latter. We then show that every -computable structure (or even just of c.e.\ degree) has the same degree spectrum as some computably enumerable (co-c.e.)\ partial order, and hence that there is a c.e.\ (co-c.e.)\ partial order with spectrum equal to the set of nonzero degrees.
Cite
@article{arxiv.1110.4068,
title = {Computably enumerable partial orders},
author = {Peter A. Cholak and Damir D. Dzhafarov and Noah Schweber and Richard A. Shore},
journal= {arXiv preprint arXiv:1110.4068},
year = {2011}
}