FOM: replacing the separation scheme
cxm7 at po.cwru.edu
Tue Jan 20 23:04:52 EST 1998
I have to apologize for a mistake in my post earlier today
where I said I was giving a replacement axiom scheme for toposes.
In fact, I gave a separation axiom scheme, and the "generalized
elements" should be "global elements".
Actually my book is the only publication I know of to
give a replacement axiom scheme. The main point is still that it
does indeed look much like the one for set theory. For any
relation R stated in the (first order, external) language of the
For any object A, if for each element x of A there is a
unique set B(x) such that x is R-related to B(x), then
there is a function g:T-->A such that the fiber of g
over any element x is the set B(x).
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