[FOM] Platonism and Formalism

Robert M. Solovay solovay at math.berkeley.edu
Sat Sep 13 17:40:17 EDT 2003

K. Kunen, Elementary embeddings and infinitary combinatorics, Journal of
Symbolic Logic, Vol. 36, (1971), pp. 407-413.

The basic point is that Friedman's axiom contradicts the axiom of choice
[by Kunen's work]. Since I hold that AC is true, it follows that (#) is
false. Of course [by well-known results of Cohen, ZF + not AC is, a
consistent theory].

	--Bob Solovay

On Fri, 12 Sep 2003, Robin Adams wrote:

> On Thu, 11 Sep 2003, Robert M. Solovay wrote:
> > I admit that I never asked him if he believed the principles in question
> > were consistent. Of course, they certainly aren't **true** by well-known
> > results of Kunen.
> Could you give a reference, please, for those of us to whom the results
> aren't so well known?  I'd be very interested to see how an axiom can be
> shown to be "certainly not true" without being proven inconsitent.
> --
> Robin Adams
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