---
tag: Z7KFSY9SRQ
kind: concept
name: Epsilon-induction
aliases: [axiom-of-epsilon-induction, axiom-of-set-induction, axiom-schema-of-epsilon-induction, axiom-schema-of-set-induction, e-induction, induction]
sources:
  - wikipedia: en:2476462@r1368260945
    locator: Epsilon-induction
    note: adopted
    mention: wikipedia://en/2476462
    sections: [Summary]
same_as:
  wikidata: Q5383944
  wikipedia: Epsilon-induction
inventory: [W3YR6S7EN3]
---

## Summary

In set theory, **$\in$-induction**, also called **epsilon-induction** or **set-induction**, is a principle that can be used to prove that all [[sets|0BSJ7RQ9BW]] satisfy a given property. Considered as an axiomatic principle, it is called the **axiom schema of set induction**.