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epsilon-induction is the scheme: $\forall x(\forall y\in x\varphi (y)\rightarrow \varphi (x))\rightarrow \forall x\varphi (x)$.

Let "bounded epsilon-induction" be the above scheme, but only for bounded formulas.

It seems clear that the full epsilon induction is not derivable from the bounded one, but I haven't managed to find a model which satisfies the bounded but not the full. If anyone can help, or refer me to some book/paper, I would appreciate it.

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    $\begingroup$ Provable over what base theory? $\endgroup$
    – Danielle Ulrich
    Commented Jun 5, 2016 at 21:54
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    $\begingroup$ Over the remaining axioms of ZF, full epsilon-induction is equivalent to its single instance with $\varphi$ being the open (hence bounded) formula $x\notin z$. $\endgroup$
    – Emil Jeřábek
    Commented Jun 5, 2016 at 22:01

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