User blog comment:Alemagno12/Defining stage n cardinals in terms of stationary sets/@comment-1605058-20180611093056/@comment-25601061-20180611151114

No. A cardinal x is hyper-Mahlo if it is x-Mahlo, so it would be stationary in the set of x-Mahlos below it, NOT the set of FIRST y-Mahlos (for all y) below it.