Ordinal collapsing function: Difference between revisions
Possibly less confusing wording
RhubarbJayde (talk | contribs) No edit summary |
(Possibly less confusing wording) |
||
Line 4:
== History ==
The first ordinal collapsing function in the literature was Bachmann's \( \psi \) 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. A modern "recast", proposed by Michael Rathjen<ref>Rathjen, Michael. "The Art of Ordinal Analysis"</ref>, is that \( \psi_\Omega(\alpha)\) is the least countable \( \rho \) so that
* Let \( \Omega = \aleph_1 \) and \( C_0^\Omega(\alpha, \beta) = \beta \cup \{0, \Omega\} \).
|