[FOM] Global well ordering versus axiom scheme of collection

[Frode Bjørdal]

I give some context for my question as background for another one which I
hope some may answer.

On Novermber 22 I posed the question Is ZF interpretable in ZF minus
extensionality plus X inaccessibles? The background is that it was shown by
Dana Scott that ZF minus extensionality does not interpret ZF when ordinary
replacement is used.

The question created interest and communication off the list. Eventually
after some scholarly work Harvey Friedman pointed me to his "The
Consistency of Classical Set Theory Relative to a Set Theory with
Intuitionistic Logic", J. of Symbolic Logic, Vol. 38, No. 2, (1973), pp.
315-319. By Theorem 1 here the theory S - which is ZF with collection,
minus extensionality and a weakened power set axiom - interprets ZF.

My question now is: Does ZF with replacement minus extensionality plus
global choice interpret ZF?

Frode

2012/8/16 Colin McLarty <colin.mclarty at case.edu>

> I have not thought about that. I don't know.
>
> Colin
>
> On Tue, Aug 14, 2012 at 3:29 PM, Frode Bjørdal
> <frode.bjordal at ifikk.uio.no> wrote:
> >
> >
> > 2012/8/14 Colin McLarty <colin.mclarty at case.edu>
> >>
> >> Over ZF[0] (which is ZF without the power set axiom), the axiom scheme
> >> of replacement does not imply that of collection.  But ZF[0] with a
> >> well ordering of the universe does, of course, since you can take the
> >> 'minimal' exemplar from each class.
> >>
> >
> > Is extensionality needed?
> >
> > --
> >
> > Frode Bjørdal
> > Professor i filosofi
> > IFIKK, Universitetet i Oslo
> > www.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
> >
> >
> >
> >
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-- 


Frode Bjørdal
Professor i filosofi
IFIKK, Universitetet i Oslowww.hf.uio.no/ifikk/personer/vit/fbjordal/index.html
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