[FOM] Global choice and ZF

[Andres Caicedo]

  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