Timothy Y. Chow tchow at alum.mit.edu
Mon Jul 19 22:17:41 EDT 2004

Jesse Alama <alama at stanford.edu> wrote:
> Some more work would be needed to conclude that most mathematicians 
> really do use classes only as figures of speech.  There is evidence for 
> the contrary position: substantial use of proper classes is made in the 
> study of universal algebra, and it seems that there classes are treated 
> as honest mathematical objects.

A couple of years ago in sci.math.research, Vidhyanath Rao argued that 
classes are sometimes used in ways that are not obviously conservative
over ZFC.  See for example


and other articles by Rao in that thread.  Rao emphasizes: "Nor is this a 
marginal example: Neeman's book is intended as a careful treatment of the 
prerequisites for Voevodsky's applications to motives."  Voevodsky, of 
course, has won the Fields medal for his work.


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