Natural well-orderings

Abstract

There seem to be at least two approaches to the problem of generating notations for ordinals: the papers of Bachmann [2], Gerber [5], Feferman [3], and Isles [6] provide examples of one and those of Ackermann [1], Takeuti [10], Kino [7], Schütte [9], and Pfeiffer [8] the other. In both of these the normal forms produced can be regarded as being finite trees “based on” some ordinal π.