[FOM] Platonism and Formalism (fwd)

Robert M. Solovay solovay at math.berkeley.edu
Wed Sep 17 01:35:38 EDT 2003

What follows is a letter of Ken Kunen answering a query raised by John

	--Bob Solovay

---------- Forwarded message ----------
Date: Tue, 16 Sep 2003 08:20:33 -0500
From: Kenneth Kunen <kunen at math.wisc.edu>
To: Robert M. Solovay <solovay at Math.Berkeley.EDU>
Cc: kunen at math.wisc.edu, John Steel <steel at Math.Berkeley.EDU>
Subject: Re: [FOM] Platonism and Formalism (fwd)


> Attached is an extract from a posting of John Steel to the FOM
> mailing list. It seems better [if you are willing] for you to comment
> rather than me. [I was present for a talk of yours at Stanford on your
> preliminary result but I don't have a clear memory of what it was.] If you
> reply to me [and give permission] I'll post your reply to the FOM list.

Sure, you have my permission.

Regarding John Steel's posting:

> I have heard the story that Kunen discovered his contradiction
> in the course of trying to strengthen Solovay's theorem that the GCH
> holds at singular strong limits above a strongly compact. Perhaps
> Bob Solovay knows whether this story is true.

He's probably referring to my proof that Reinhardt's Axiom
is contradictory: J. Symbolic Logic, Vol. 36 (1971), pp. 407-413.
My original result was that Reinhardt's Axiom contradicted the GCH.
I actually have a letter from you written in 1969, commenting on
that result, and you said, among other things,
"Perhaps Reinhardt's axiom is inconsistent?"
You also pointed out that the axiom was due to Reinhardt;
I had been calling it "Solovay's Axiom".


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