[FOM] Re: WHY DO SET THEORISTS DISLIKE CHRIS FREILING'S EVIDENCE AGAINST THE CONTINUUM HYPOTHESIS?
Robert M. Solovay
solovay at math.berkeley.edu
Thu Sep 2 13:25:15 EDT 2004
On Thu, 2 Sep 2004, Timothy Y. Chow wrote:
[snip]
>
> A less formal but maybe more striking way to put it is that since the
> axiom of choice implies something as weird as the Banach-Tarski paradox,
> what's to stop it from implying something as weird as the continuum
> hypothesis?
>
Cohen proved in the early 60's that the Axiom of Choice does not
imply the Continuum Hypothesis. Godel had shown in the 30's that the axiom
of choice does not imply the negation of CH.
Both results are in the context of ZF, Both assume the hypothesis
that ZF is consistent. Kunen's text on set theory presents these results.
--Bob Solovay
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