FOM: Grothendieck universes
kanovei at wmfiz1.math.uni-wuppertal.de
Mon Apr 19 15:51:45 EDT 1999
> Date: Sat, 17 Apr 1999 18:21:37 -0400 (EDT)
> From: cxm7 at po.cwru.edu (Colin Mclarty)
> I have mentioned a restriction that will work for all
> of Grothendieck's purposes, namely to V(w+w) but ...
I do not know much about what things like
*derived functor cohomology* are, but still some
conclusions from the ongoing discussion can be
1) To carry out some complicated proofs in
*serious number theory* in natural way, one needs
complicated systems of algebraic objects, closed
under certain operations.
2) Any V_a, where a>w is a limit ordinal, can be taken
as a *universe* within which all necessary operations
can be carried out.
3) Therefore, the results obtained are ZFC results,
that4s it, which keeps the integrity of mathematics.
4) A mathematician
(perhaps except of those who are just interested
in the category theory for its own sake)
would like to obtain practically more
elementary proofs of number theoretic results,
at least such proofs which do not involve
more complicated objects than Borel sets in
Polish spaces, or ultimately pure PA proofs.
More information about the FOM