Minimal idempotent ultrafilters and the Auslander-Ellis theorem

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 ${\Pi }_2^1$-conservative over a refinement of AET.

Cited by in corpus (1)

• Arrow's theorem, ultrafilters, and reverse mathematics