[FOM] Why would one prefer ZFC to ZC?

[Harvey Friedman]

On Jan 26, 2010, at 5:09 PM, Jeremy Bem wrote:

> Why would someone prefer ZFC? [over ZC)

One reason to consider:

THEOREM. Every Borel set in the Euclidean plane = RxR, symmetric about  
the line y = x, contains or is disjoint from the graph of a Borel  
function from R into R.

The above theorem is provable in ZFC but not in ZC.

Harvey Friedman