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MoeBlee wrote:
> Rupert wrote:
> > MoeBlee wrote:
> > > For ZC (Z set theory with the axiom of choice), I'm pretty sure I see
> > > how to prove:
> > >
> > > AxEy(x equinumerous with y & x/\y = 0)
> > >
> > > where '/\' stands for binary intersection.
> > >
> > > But can this be proven without the axiom of choice? If so, how to do
> > > it?
> > >
> >
> > Yes, consider x X {x}.
>
> Of course I thought of that. But that doesn't the disjointedness
> require the axiom of regularity? I should have been clear to exclude
> use of regularity also. So the axioms are
>
> extensionality
> separation
> pair
> union
> power
> infinity (though, I'd like to exclude it also)
>
> Thanks,
>
> MoeBlee
I'd be interested to see your proof that uses the axiom of choice but
doesn't use regularity.
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