[FOM] Replacement

Thomas Forster T.Forster at dpmms.cam.ac.uk
Thu Aug 16 19:19:33 EDT 2007

Well, it depends on your implementation of pairing.  Cartesian products
can be poroved to exist in Zermelo set theory if you use Winer-Kuratowski
pairs.  Mathias has a delightful short proof that replecement follows from
the assertion that the cartesian produc x \times y exists for all x and y
and all implementations of pairing.

On Thu, 16 Aug 2007, Jan Pax wrote:

> Even the existence of cartesian product requires replacement.
> Correct me if I'm false.
>
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