Shipman's schema for ZF(C)
Zvonimir Sikic
zvonimir.sikic at gmail.com
Sun Aug 29 04:48:31 EDT 2021
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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