---
tag: 3385N1A51V
kind: concept
name: Difference hierarchy
sources:
  - wikipedia: en:3893531@r958790728
    locator: Difference hierarchy
    note: adopted
    mention: wikipedia://en/3893531
    sections: [Summary]
same_as:
  wikidata: Q5275274
  wikipedia: Difference hierarchy
inventory: [FNFD1R6R4W]
---

## Summary

In set theory, a branch of mathematics, the **difference hierarchy** over a pointclass is a hierarchy of larger pointclasses generated by taking [[differences|0RKF1ZT5JJ]] of sets. If Γ is a pointclass, then the set of differences in Γ is $\{A:\exists C,D\in\Gamma ( A = C\setminus D)\}$. In usual notation, this set is denoted by 2-Γ. The next level of the hierarchy is denoted by 3-Γ and consists of differences of three sets: $\{A : \exists C,D,E\in\Gamma ( A=C\setminus(D\setminus E))\}$. This definition can be extended recursively into the transfinite to *α*-Γ for some [[ordinal|0RDJK7EQYY]] *α*.