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Rupert wrote:
> If ZF is consistent, then the proposition that the set of functions
> from the reals to the reals can be totally ordered is indepedent of ZF.
> Cohen proved this at the same time as he proved the independence of the
> continuum hypothesis. See "Set Theory and the Continuum Hypothesis".
I had a hunch it was in the Cohen package. Thanks for confirming.
>
> > And what about "every set can be partially ordered"?
> >
>
> I would think this is provable, consider the transitive closure of the
> membership relation.
Isn't partial ordering as simple as observing (as I did in my second
post) that the subset relation is a partial ordering? But I'll think
about transitive closure too (I need to study that concept anyway).
Thanks,
MoeBlee
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