[FOM] Global choice and ZF

[T.Forster@dpmms.cam.ac.uk]

So the theory pf the set part of a model of NGB + global choice is 
precisely ZFC. Global choice gives a conservative extension?

On Apr 2 2009, Andres Caicedo wrote:

>
>  Hi Thomas,
>
>> Am i right in thinking that ZF + V = HOD is the theory of the set-part 
>> of a model of NGB+globalchoice?
>
>  No, this is not the case. In fact, one can add a global choice function 
>by proper class forcing over any model of ZFC without adding any sets. 
>(This is actually useful in some settings.)
>
>  Best,
>  Andres
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