[FOM] Arithmetical soundness of ZFC (platonic)

[Timothy Y. Chow]

Panu Raatika wrote:
> Set theoretical arguments - not arguments in "actual mathematical  
> practice". The reason I press this is that Cantorian set theory was,  
> at the time, extremely controversial, and I just feel it is misleading  
> to count it, at the time, as "actual mathematical practice". But this  
> is probably just a verbal issue...

The distinction isn't so important in the context of my reply to Weaver. 
But now you've got me curious in the historical question of how Zermelo 
set theory and its variants arrived at its current status.  When and how 
did it become widely accepted that all of mathematics could be based on 
set theory?  Obviously Bourbaki was an important influence, but surely 
there were other currents?  For example, Bourbaki didn't use ZFC in its 
current form.

Tim