Alternative axiom scheme for ZF(C)

[Peter Koepke]

The proposed scheme does not have strength: if you assume that every set 
is an element of a set (Forall x Exists y (x in y)), then the scheme 
follows immediately.

Peter Koepke

On 27.08.21 06:02, JOSEPH SHIPMAN 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
>
>