Shipman's schema for ZF(C)

[Zvonimir Sikic]

As noted by Carnerio and, in one direction, by Kepke, Shipman's schema is
equivalent to Ay Ex (y in x). Hence, the schema is more akin to Peano's
axiom  Ay Ex (x succeeds y) then to the induction. Is it possible that
Shipman meant

Ax (Ay (y in x -> S(y)) -> S(x)) -> Az S(z)

instead of

Ax (Ay (y in x -> S(y))            ) -> Az S(z)?

On Fri, Aug 27, 2021 at 11:26 AM JOSEPH SHIPMAN <joeshipman at aol.com> wrote:

> Consider the set induction scheme:
>
> (Forall x Forall y (y in x implies Phi(y))) implies (Forall z Phi(z))
>
> With this included, which other axioms of ZFC may be dispensed with?
>
> ? JS
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