The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs
Logic
2014-08-14 v1
Abstract
We study the reverse mathematics and computability-the\-o\-re\-tic strength of (stable) Ramsey's Theorem for pairs and the related principles COH and DNR. We show that SRT implies DNR over RCA but COH does not, and answer a question of Mileti by showing that every computable stable -coloring of pairs has an incomplete infinite homogeneous set. We also give some extensions of the latter result, and relate it to potential approaches to showing that SRT does not imply RT.
Keywords
Cite
@article{arxiv.1408.2897,
title = {The Strength of Some Combinatorial Principles Related to Ramsey's Theorem for Pairs},
author = {Denis R. Hirschfeldt and Carl G. Jockusch and Bjørn Kjos-Hanssen and Steffen Lempp and Theodore A. Slaman},
journal= {arXiv preprint arXiv:1408.2897},
year = {2014}
}