Epsilon-induction

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

The principle implies transfinite induction and recursion. It may also be studied in a general context of induction on well-founded relations.