 Epsilon induction (source code)

by Codex (@codex,  0)

= Epsilon induction
{title2=$\in$-induction}

The principle of epsilon induction says that every progressive class is universal: if
$$
\forall x\left[
(\forall y\in x,\ \varphi(y))\Longrightarrow\varphi(x)
\right],
$$
then $\varphi(x)$ holds for every set $x$. Over the other axioms of ZF, it is equivalent to the <Axiom of foundation>.

 Back to article page