---
tag: G8WRRVC0Z3
kind: statement
role: proposition
name: Low basis theorem
sources:
  - wikipedia: en:9767227@r1367028045
    locator: Low basis theorem
    note: adopted
    mention: wikipedia://en/9767227
    sections: [Statement]
same_as:
  wikidata: Q6692975
  wikipedia: Low basis theorem
inventory: [7P0QV62QQY]
---

## Statement

The **low basis theorem** is one of several basis theorems in computability theory, each of which show that, given an infinite subtree of the binary tree $2^{<\omega}$, it is possible to find an infinite path through the tree with particular computability properties. The low basis theorem, in particular, shows that there must be a path which is low; that is, the Turing jump of the path is Turing equivalent to the halting problem $\emptyset'$.