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Topic: unable to prove?
Replies: 28   Last Post: Sep 18, 2012 3:54 PM

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 Michael Stemper Posts: 671 Registered: 6/26/08
Re: unable to prove?
Posted: Aug 28, 2012 8:53 AM

In article <k1gri5\$k9d\$1@dont-email.me>, "dilettante" <no@nonono.no> writes:
>"Michael Stemper" <mstemper@walkabout.empros.com> wrote in message news:k1g8tg\$jql\$1@dont-email.me...
>> In article <k1aqov\$3b9\$1@dont-email.me>, "dilettante" <no@nonono.no> writes:

>>> This has always been a little disconcerting for me. I've read that it was
>>>proved that CH is independent of the usual axioms of set theory, or
>>>something like that. It seems to me that if the real numbers are a well
>>>defined object, then its power set should be a well defined object, and it
>>>should be the case that either some member of that power set has
>>>cardinality
>>>between that of the naturals and that of the reals, or not. If such an
>>>animal did exist, it should be at least possible for someone to exhibit it
>>>in some way - "here it is, now what about that independence?"

>>
>> I asked a very similar question here eighteen years back (give or take
>> a month). One Mike Oliver responded:
>>
>> =================================================================

>>>Although CH is independent of ZF, isn't it still possible that
>>>somebody could find a set that violates it?

>>
>> It depends on what you mean by "find." It is not possible to define
>> a set of reals and prove *in ZFC* that it has cardinality strictly
>> between that of the integers and that of the real numbers.
>>
>> But you might be able to define a set that "really" has this property,
>> even though not provably in ZFC.
>> =================================================================

>
>Interesting. I suppose the question of what this "really" consists of is one
>of those foundational questions that don't have an answer that is
>universally accepted.

That would be my guess, as well.

--
Michael F. Stemper
#include <Standard_Disclaimer>
Life's too important to take seriously.

Date Subject Author
8/24/12 ts742
8/24/12 ma'ayan peres
8/24/12 Frederick Williams
8/25/12 David C. Ullrich
8/25/12 Frederick Williams
8/25/12 dilettante
8/25/12 Frederick Williams
8/27/12 dilettante
8/27/12 David C. Ullrich
8/27/12 dilettante
8/27/12 Frederick Williams
8/27/12 dilettante
8/28/12 Michael Stemper
8/28/12 Frederick Williams
8/28/12 David C. Ullrich
8/28/12 dilettante
8/28/12 Frederick Williams
8/27/12 Frederick Williams
8/27/12 Frederick Williams
8/27/12 Michael Stemper
8/27/12 dilettante
8/28/12 Michael Stemper
9/1/12 David Bernier
9/2/12 Herman Rubin
9/18/12 Herman Rubin
8/28/12 Frederick Williams
8/25/12 Pfsszxt@aol.com
9/5/12 HOPEINCHRIST
9/6/12 Luis A. Rodriguez