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From: ndiamond@watdaisy.UUCP (Norman Diamond)
Newsgroups: net.math
Subject: Re: Re: Nova's Mathematical Mystery Tour
Message-ID: <7061@watdaisy.UUCP>
Date: Tue, 12-Mar-85 13:48:11 EST
Article-I.D.: watdaisy.7061
Posted: Tue Mar 12 13:48:11 1985
Date-Received: Wed, 13-Mar-85 00:11:56 EST
References: <143@ihlpa.UUCP> <460@petsd.UUCP> <6353@boring.UUCP> <350@talcott.UUCP>
Organization: U of Waterloo, Ontario
Lines: 28

> > ... it is conceivable (although highly implausible) that someone will some
> > day come up with new methods of mathematical reasoning that are *obviously*
> > valid, using which CH can be decided.
> > --  Lambert Meertens
>
> Really?  I had always thought that there were two "classes" of sets:  in
> one class, the CH is true, and in the other it is false.
> ... Or is this duality valid in the first place?
> --  Greg Kuperberg

That duality is valid in ZF set theory.  It is conceivable (although highly
implausible) that someone will some day come up with a new set theory, that
will be *obviously* valid, that will not be ZF set theory.  It would have
different axioms and a different set of provable theorems.  Obviously 8-)-----
most of the theorems will be the same as today's, but....
                                                                         ^
                                                                         |
                                                 (that's sticking my neck out)

-- 

   Norman Diamond

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