  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^+.
