FOM: topos theory qua f.o.m.

[Colin Mclarty]

Reply to message from simpson at math.psu.edu of Fri, 16 Jan
>

>"In-principle", we
>all know how to set up real analysis in ZFC.  But to me at least, it's
>not so clear how to set it up in elementary topos theory, even
>"in-principle".  Recall that some developments of intuitionistic
>analysis are horribly messy and seem to leave us with no way to obtain
>even the standard rudiments of engineering mathematics.
>
>In the meantime, McLarty has stated definitively that elementary topos
>with a natural number object is the correct setting for this kind of
>real analysis.                                        ^^^^^^^^^^^^^^ 

	Which kind of real analysis do you mean now? The rudiments of
engineering analysis? analysis in ZFC? intuitionistic analysis?

	These are very different things, as you know well from your
own Reverse Mathematics. So which one am I supposed to have said can be
done in any topos with natural numbers?

Colin