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This is a translation of Heinz Bachmann's influential paper, wherein theBachmann-Howard ordinal is defined, and some general considerations given onsystems of ordinal functions. Permission to post has been granted by theeditors of Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich(www.ngzh.ch)

A Translation of "Die Normalfunktionen und das Problem der ausgezeichneten Folgen von Ordnungszahlen" by Heinz Bachmann