On 08/03/2011 06:07 PM, Darren New wrote:
>> Wasn't the question whether there is a set that is larger than a
>> countable
>> infinite set and smaller than an uncountable infinite set proven to be
>> unprovable?
>
> My memory is that it was thought to be unprovable but later proven to
> not be so. However, wikipedia (Cardinal_numbers) agrees with you. Not
> that it's unprovable, but that its provability depends on the axioms of
> set theory you accept. I suspect it depends in part on things like the
> axiom of choice, etc.

That was my recollection - that the question is provably "independent" 
of the standard axioms of set theory. (I believe the axiom of choice is 
specifically implicated - although I have no idea WTF the axiom of 
choice is.)

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