[FOM] Mac lane set theory

Thomas Forster T.Forster at dpmms.cam.ac.uk
Mon Dec 21 12:27:58 EST 2009

Adam Epstein has just prompted me to look at section 9 of Mathias' ``On 
the strength of Mac lane Set theory'' in this connection.  It is online at


On Sun, 20 Dec 2009, 
joeshipman at aol.com wrote:

> 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
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