Buchholz's psi-functions: Difference between revisions
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(Created page with "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 source...") |
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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. |
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. |
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==Historical background== |
==Historical background== |
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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 |
In 1950, H. Bachmann defined the first ordinal collapsing function, Bachmann's \(\varphi\). While able to succinctly describe the Bachmann-Howard ordinal as \(\varphi_{\varepsilon_{\Omega+1}}(0)\){{citation needed}}, Bachmann's \(\varphi\) had a complicated definition |
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Possible sources for this section: |
Possible sources for this section: |
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Revision as of 02:33, 29 November 2022
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 \(\varphi_{\varepsilon_{\Omega+1}}(0)\)[Citation needed], 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.