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

TL;DR

This paper provides a translation of Heinz Bachmann's influential work, introducing the Bachmann-Howard ordinal and discussing systems of ordinal functions, which are fundamental in proof theory and ordinal analysis.

Contribution

It presents the first English translation of Bachmann's seminal paper, clarifying the definition of the Bachmann-Howard ordinal and exploring properties of ordinal function systems.

Findings

Definition of the Bachmann-Howard ordinal

Insights into systems of ordinal functions

Foundational contributions to proof theory

Abstract

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