[FOM] Global Choice

Robert Solovay solovay at gmail.com
Mon Apr 5 20:48:56 EDT 2010


The answer is yes. The result is due to a lot of people (including
Jensen and myself). Basically one forces to add a generic
well-ordering of the universe without adding new sets. Felgner
published this in 1971:
 F. published this. (Fund, Math, 71(1971), pp. 43--62)

I  also  found the following relevant paper of Gaifman:

 Global and local choice functions
Journal	Israel Journal of Mathematics
Issue	Volume 22, Numbers 3-4 / December, 1975
Pages	257-265

Global and local choice functions

Abstract  We prove, by an elementary reflection method, without the
use of forcing, that ZFGC (ZF with a global choice function) is a
conservative extension of ZFC and that every model of ZFC whose
ordinals are cofinal (from the outside) withω can be expanded to a
model of ZFGC (without adding new members). The results are then
generalized to various weaker forms of the axiom of choice which have
global versions.

--Bob Solovay

On Mon, Apr 5, 2010 at 1:42 AM,  <T.Forster at dpmms.cam.ac.uk> wrote:
> Is Goedel-Bernays + global choice a conservative extension of ZFC..?
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