---
tag: S5FTQGHVKC
kind: concept
name: Takeuti–Feferman–Buchholz ordinal
sources:
  - wikipedia: en:68444579@r1358903135
    locator: Takeuti–Feferman–Buchholz ordinal
    note: adopted
    mention: wikipedia://en/68444579
    sections: [Summary]
same_as:
  wikidata: Q108266145
  wikipedia: Takeuti–Feferman–Buchholz ordinal
inventory: [TVJC8SV71P]
---

## Summary

In the mathematical fields of set theory and proof theory, the **Takeuti–Feferman–Buchholz ordinal (TFBO)** is a large countable ordinal, which acts as the limit of the range of Buchholz's psi function and Feferman's theta function. It was named by David Madore, after Gaisi Takeuti, Solomon Feferman and Wilfried Buchholz. It is written as $\psi_0(\varepsilon_{\Omega_\omega + 1})$ using Buchholz's psi function, an ordinal collapsing function invented by Wilfried Buchholz, and $\theta_{\varepsilon_{\Omega_\omega + 1}}(0)$ in Feferman's theta function, an ordinal collapsing function invented by Solomon Feferman. It is the proof-theoretic ordinal of several formal theories: