[FOM] Mac lane set theory

[joeshipman@aol.com]

Can anyone provide an example of a statement of "ordinary mathematics" 
which can be proved in Zermelo set theory but not MacLane set theory?  
I can understand that one might imagine the subject matter of ordinary 
mathematics to be contained in a finitely iterated powerset of the 
integers, but why would one then choose MacLane over Zermelo?

-- JS

-----Original Message-----
From: Thomas Forster <T.Forster at dpmms.cam.ac.uk>

There is a body of opinion out there (i suspect not represented on FOM
but...) that holds that Ordinary Mathematics can be captured by Mac 
lane
set theory (the fragment of Zermelo set theory with Delta-0 separation
instead of full separation)....  I suspect the thought is merely that 
mathematics is to be
identified with the nth order theory of the reals/complexes for n
arbitrarily large, but it might be more interesting than that