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$\left( {{{\cal U}_{{\rm{idem}}}}} \right)$
be the statement that an idempotent ultrafilter on ℕ exists. We show that over 
$ACA_0^\omega$
, the higher-order extension of ACA0, the statement 
$\left( {{{\cal U}_{{\rm{idem}}}}} \right)$
implies the iterated Hindman’s theorem (IHT) and we show that 
$ACA_0^\omega + \left( {{{\cal U}_{{\rm{idem}}}}} \right)$
is 
${\rm{\Pi }}_2^1$
-conservative over 
$ACA_0^\omega + IHT$
and thus over 
$ACA_0^ +$
.
