[FOM] Global Choice

T.Forster@dpmms.cam.ac.uk T.Forster at dpmms.cam.ac.uk
Tue Apr 6 02:51:40 EDT 2010

Thanks to all who replied, for prompt and informative answers!

On Apr 6 2010, Robert Solovay wrote:

>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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