A generalization of Malho's method for obtaining large cardinal numbers

Mahlo used a method by which fixed points of an enumeration of regular cardinals were employed to get a hierarchy of "large cardinals." He also employed a second method which, in a certain sense, is much stronger than the first. Here the methods are investigated and generalized and the relations between them are clarified. This stronger method turns out to be a kind of "least upper bound" to all "fixed-points operations." Possibilities of strengthening these processes in a natural way are pointed out.