[FOM] Replacement

Harvey Friedman friedman at math.ohio-state.edu
Mon Aug 13 16:23:22 EDT 2007

On 8/13/07 3:08 AM, "Thomas Forster" <T.Forster at dpmms.cam.ac.uk> wrote:

> I know there are lots of people who dislike the axiom scheme of
> replacement.  They say things like ``it has no consequence for
> ordinary mathematics'' and the like.  Unfortunately i have none
> of them handy at the moment, so i have to ask:  do any of them
> think that the axiom scheme is actually *false*?  Or do they
> merely think that it shouldn't be a core axiom?
>    tf

"Every symmetric Borel set in the plane contains or is disjoint from the
graph of a Borel function"

can be proved in ZFC but not in ZFC\Replacement.

Harvey Friedman

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