[FOM] Re: AXIOM SCHEMATA

[Timothy Y. Chow]

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

http://www.google.com/groups?selm=aklihk%24j5j%243%40charm.magnus.acs.ohio-state.edu

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.

Tim