On idempotent ultrafilters in higher-order reverse mathematics
  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^+. 
Alexander P. Kreuzer
math.LO