Re: The real numbers, and general comments

From: Dave Seaman (dseaman_at_no.such.host)
Date: 10/05/04 

Date: Tue, 5 Oct 2004 12:40:05 +0000 (UTC)

On 4 Oct 2004 21:04:58 -0700, Andrew Usher wrote:
> Dave Seaman <dseaman@no.such.host> wrote in message news:<cjqcb5$2uo$1@mozo.cc.purdue.edu>...

>> > Cantor's power-set theorem can be proved using real logic, as
>> > Cantor did; it can also be 'proved' in ZF.
>>
>> It's an axiom of ZF.

> No, a theorem. The PS axiom doesn't assert P(A) > A.

I meant that the power set axiom is an axiom of ZF. That is what the theorem
is based on.

>> > But (I think) Lowenheim-Skolen says that a bijection does exist, but
>> > ZFC can't find it. Now if L-S says only that 'there exist countable
>> > models', no problem; but I amd not sure which.
>>
>> That's not what L-S says. L-S is about models, and Cantor's theorem does
>> not make reference to any particular model.

> The version of Cantor not using a model is therefore not ZF.

Non sequitur. ZF does not make any reference to models. 

-- 
Dave Seaman
Judge Yohn's mistakes revealed in Mumia Abu-Jamal ruling.
<http://www.commoncouragepress.com/index.cfm?action=book&bookid=228>

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