FOM: topos theory
kanovei at wminf2.math.uni-wuppertal.de
Fri Jan 16 06:57:41 EST 1998
It follows from McLarty's post that pumping
enough ZFC into a topos we get inside the
topos "reals" adequate for this or that
purpose, for instance those not satisfying
the excluded middle.
However mathematiciands working with *bridges*
(which by Simpson means real analysis in its
classical form) pretend to work with THE reals,
i.e. something uniquely determined by the very
basic nature of mathematics (if not by the
It is a great advantage of set theory that it
grounds and supports this approach.
Does the topos theory do this ?
Hopefully McLarty could address this question.
But the expected answer amounts to the following:
*take a "category of sets" or a "topos well pumped
by ZFC" and go ahead*.
If so then the total picture is not inspiring.
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