Alternative axiom scheme for ZF(C)

Peter Koepke koepke at math.uni-bonn.de
Sat Aug 28 12:48:47 EDT 2021


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
>
>


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