[FOM] Global choice and ZF

[Allen Hazen]

I've never read it, but you might find relevant information in Ulrich
Felgner, "Choice functions on sets and classes" (pp. 217-255 in Gert Müller,
ed., "Sets and Classes," Amsterdam: North-Holland, 1976: this is the yellow
"Studies in Logic" volume that contains the reprinting of Bernays's JSL
articles).  Corollary 4.1 (p. 243) says a sentence in the language of ZF is
provable in ZF + (local) Choice iff it is provable in NB + (global) Choice.

It is assumed in this that ZF and NB include the Axiom of Foundation:
apparently things are -- or at least in 1976 were -- a bit dicier in the
absence of foundation.  (We don't know anyone interested in systems without
foundation, though, do we?)

I really must get around to reading this some day: I thought I had a REALLY
easy proof of the result, but if it merited an article of this length I must
have overlooked some essential complication!
--
Allen Hazen
Philosophy (PASI)
University of Melbourne


On 3/4/09 7:01 PM, "T.Forster at dpmms.cam.ac.uk" <T.Forster at dpmms.cam.ac.uk>
wrote:

> The feedback I am getting suggests that the truth of the matter is that
> 
> NGB + global choice is an extension of NGB + set choice that is
> conservative for the language of pure sets.
> 
>  Can anyone confirm this, preferably with a reference?