Buchholz's psi-functions
Buchholz's \(\psi\)-functions are a family of functions \(\psi_\nu:(\omega+1)\times\textrm{Ord}\to\textrm{Ord},\;\alpha\mapsto\psi_\nu(\alpha)\) defined by Wilfried Buchholz in 1984.
Historical background
In 1950, H. Bachmann defined the first ordinal collapsing function, Bachmann's \(\varphi\). While able to succinctly describe the Bachmann-Howard ordinal as \(\varphi_{\varepsilon_{\Omega+1}}(0)\), Bachmann's \(\varphi\) had a complicated definition
Possible sources for this section:
- M. Rathjen, The Art of Ordinal Analysis
- W. Buchholz, A survey on ordinal notations around the Bachmann-Howard ordinal
- About Bridge's work on Feferman theta: W. Buchholz, Relating ordinals to proofs in a perspicuous way
- About the conception of Feferman theta, and some more historical detail on pre-Feferman OCFs: S. Feferman, The proof theory of classical and constructive inductive definitions. A 40 year saga, 1968-2008.