Re: no fundamental theorems please

[Martin Escardo <m.escardo@cs.bham.ac.uk>]

I am sure several other readers of this list will have the same reply
to this specific point of Paul's message:

Paul Taylor wrote:
> For example, there is Cantor's "theorem" about a powerset being
> strictly bigger than a set.  This belongs entirely to the dogma
> of set theory.  When set theory is overturned, this miserable
> and wholely misguided "theorem" will go in the dustbin of
> mathematical history with it.

There is a very nice paper by Lawvere that shows that the essence of
Cantor's theorem is fundamental and beautiful:

   Originally published in: Diagonal arguments and cartesian closed
   categories, Lecture Notes in Mathematics, 92 (1969), 134-145.

   Reprinted in TAC:

   http://www.tac.mta.ca/tac/reprints/articles/15/tr15abs.html

There is also a post by Andrej Bauer in his Mathematics and
Computation blog:

   http://math.andrej.com/2007/04/08/on-a-proof-of-cantors-theorem/

Martin



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