[FOM] Error in statement of AC

Kurt Maes maes.kurt at pandora.be
Thu Nov 6 07:51:09 EST 2003

Matt Insall claimed that the statement

> (GC)  There is a class whose intersectoin with every nonempty set is a
> singleton.

is equivalent to the axiom of global choice.
I'm sorry to inform you that this statement below is still not a form of GC 
because it is inconsistent.
Suppose this class exists and call it G, then for all singletons {a}, G 
contains a, so G contains all sets. So {a,b} intersection G = {a,b}, which 
is not a singleton and thus in contradiction with the definition of G.

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