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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
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