Minimal idempotent ultrafilters and the Auslander-Ellis theorem
Logic
2015-10-12 v2
Abstract
We characterize the existence of minimal idempotent ultrafilters (on N) in the style of reverse mathematics and higher-order reverse mathematics using the Auslander-Ellis theorem and variant thereof. We obtain that the existence of minimal idempotent ultrafilters restricted to countable algebras of sets is equivalent to the Auslander-Ellis theorem (AET) and that the existence of minimal idempotent ultrafilters as higher-order objects is -conservative over a refinement of AET.
Keywords
Cite
@article{arxiv.1305.6530,
title = {Minimal idempotent ultrafilters and the Auslander-Ellis theorem},
author = {Alexander P. Kreuzer},
journal= {arXiv preprint arXiv:1305.6530},
year = {2015}
}