---
tag: CS9FHV1F3S
kind: concept
name: Buchholz hydra
sources:
  - wikipedia: en:68638522@r1342503229
    locator: Buchholz hydra
    note: adopted
    mention: wikipedia://en/68638522
    sections: [Summary]
same_as:
  wikidata: Q108582264
  wikipedia: Buchholz hydra
inventory: [103C865Q77]
---

## Summary

In mathematics, especially mathematical logic, graph theory and number theory, the **Buchholz hydra game** is a type of hydra game, which is a single-player game based on the idea of chopping pieces off a [[mathematical tree|062D9KXJB1]]. The hydra game can be used to generate a rapidly growing [[function|0EPAT51DXQ]], $BH(n)$, which eventually dominates all recursive functions that are provably total in "$\textrm{ID}_{\nu}$", and it is not provable that all hydra games terminate in $\textrm{(}\Pi_1^1\textrm{-CA)+BI}$.