Ordinal collapsing function: Difference between revisions

The first ordinal collapsing function in the literature was Bachmann's \( \psivarphi \) function, which was regarded as novel at the time and was used to calibrate the size of the [[Bachmann-Howard ordinal]]. However, the definition is quite cumbersome. Bachmann's method was extended to use higher cardinals, e.g. to use \(\Omega_n\) for all finite \(n\) by Pfeiffer in 1964 and to use \(\Omega_\alpha\) for \(\alpha<I\) by Isles in 1970,<ref>Buchholz, Feferman, Pohlers, Sieg, ''Iterated Inductive Definitions and Subsystems of Analysis: Recent Proof-Theoretical Studies''. Lecture Notes in Mathematics (1981). Springer Berlin Heidelberg, ISBN 9783540386490.</ref> but with similarly cumbersome definitions.<ref name="RathjenArt" />^p.11