Re: Two neat facts from set theory
From: Stephen J. Herschkorn (sjherschko_at_netscape.net)
Date: 01/01/05
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Date: Sat, 01 Jan 2005 12:42:56 -0500
Butch Malahide wrote:
>Butch Malahide wrote:
>
>
>>Stephen J. Herschkorn wrote:
>>
>>
>>>In that thread, my argument for singular cardinals invokes the
>>>
>>>
>axiom
>
>
>>of
>>
>>
>>>choice. Can you provide an argument that avoids it?
>>>
>>>
>
>
>
>>I hope so, but I haven't done it yet. Let me get back to you on that.
>>
>>
>
>No, I can't. Without the axiom of choice, I don't even see how to prove
>it for the case X = omega_1 (which could be singular), do you?
>Sorry for posting nonsense.
>
I was about to say that as an successor cardinal, omega_1 is regular.
But now I realize that even that fact relies on AC. So I guess I don't.
HNY to you, too!
-- Stephen J. Herschkorn sjherschko@netscape.net
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