Alternative axiom scheme for ZF(C)

Mario Carneiro di.gama at
Fri Aug 27 17:49:58 EDT 2021

That axiom is equivalent to

forall y exists x (y in x)

from which one can derive the existence of singletons (via the subset
axiom) and not much else. Considering that singletons are usually derived
from the axiom of pairing, I don't think it will eliminate any normal ZFC

Mario Carneiro

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