On idempotent ultrafilters in higher-order reverse mathematics
Logic
2015-04-09 v2
Abstract
We analyze the strength of the existence of idempotent ultrafilters in higher-order reverse mathematics. Let (Uidem) be the statement that an idempotent ultrafilter on the natural numbers exists. We show that over ACA_0^w, the higher-order extension of ACA_0, the statement (Uidem) implies the iterated Hindman's theorem (IHT), and we show that ACA_0^w + (Uidem) is Pi^1_2-conservative over ACA_0^w + IHT and thus over ACA_0^+.
Keywords
Cite
@article{arxiv.1208.1424,
title = {On idempotent ultrafilters in higher-order reverse mathematics},
author = {Alexander P. Kreuzer},
journal= {arXiv preprint arXiv:1208.1424},
year = {2015}
}