Re: infinity

Martin Shobe wrote:
> I consider this an example of where the reliance on set theory has
> hurt mathematics. Whether or not the objects form a set, is rather
> peripheral to what a ring is. (How often do you actually use the set
> part of the definition?)

All the proofs of theorems I know from algebra use some properties of
sets. Now perhaps some theorems would be OK with a proper class of
objects rather then a set, but this is quite subtle to argue through.
If you assume a set then you can do pretty much naive set theory in
your proofs since you are always working with sets.

Do you know of a proper class of objects where it would be useful to
define a ring?

Jiri

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