[FOM] Replacement
Saurav Bhaumik
saurav1b at gmail.com
Tue Aug 14 01:05:33 EDT 2007
Exactly, I have the same thing to point here: can the existence of
Hartogs function proved without Replacement?
Another thing:
Consider the statement: If F: On --> P(S) be an increasing function,
where P(S) is the power set of non-empty S; then f(a) = f(a+) for some
ordinal a.
Can the above proved without Replacement? Or is there a counterexample
in ZF - Replacement ?
Saurav
> E.g. with replacement, every well ordered set is isomorphic to a (unique) ordinal.
> JP
>
> > I know there are lots of people who dislike the axiom scheme of
> > replacement. They say things like ``it has no consequence for
> > ordinary mathematics'' and the like. Unfortunately i have none
> > of them handy at the moment, so i have to ask: do any of them
> > think that the axiom scheme is actually *false*? Or do they
> > merely think that it shouldn't be a core axiom?
> >
> > tf
> >
> >
> > --
> > Home page: www.dpmms.cam.ac.uk/~tf; dpmms phone +44-1223-337981.
> > In NZ until october work ph +64-3367001 and ask for extension 8152.
> > Mobile in NZ +64-21-0580093 (Mobile in UK +44-7887-701-562).
> >
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> >
> >
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