[FOM] A little trouble with definition of "binary relation" in Wikipedia (fwd)

William Tait williamtait at mac.com
Thu Feb 1 10:09:43 EST 2007

Ax{0}uBx{1} will work for the ordered pair of A and B.

Bill Tait

On Jan 31, 2007, at 8:33 PM, Robert M. Solovay (by way of Martin  
Davis	<martin at eipye.com>) wrote:

> This doesn't work. The cartesian product of two factors [at least one
> of which is the null set] is null.
>          --Bob Solovay
> On Mon, 29 Jan 2007, Thomas Forster wrote:
>> Yes, there are such theories but you don't need them. (In  
>> particular you
>> don't need to know about Ackermann set theory!)  When you want an  
>> ordered
>> pair of two NBG-style proper classes, use their (Wiener-Kuratowski)
>> cartesian product instead: there is nothing sacred about the
>> Wiener-Kuratowski implementation of pairing and unpairing.
>> If you are unhappy about having a different implementation of
>> pairing-and-unpairing for sets and for proper classes, then use  
>> the same
>> (cartesian-product-using-W-K-pairs) for both!
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