[FOM] Replacement

[Saurav Bhaumik]

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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