On idempotent ultrafilters in higher-order reverse mathematics
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 ACA0w, the higher-order extension of ACA0, the statement (Uidem) implies the iterated Hindman's theorem (IHT), and we show that ACA0w + (Uidem) is Pi12-conservative over ACA0w + IHT and thus over ACA0+.
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