Re: Zorn's lemma for families of subsets of a countable set
From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 06/23/04
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Date: Wed, 23 Jun 2004 06:19:39 -0500
On 23 Jun 2004 00:10:48 -0700, kramsay@aol.com (Keith Ramsay) wrote:
>Is the special case of Zorn's lemma where the ordered
>set consists of a family of subsets of a countable set,
>ordered by inclusion, a theorem of ZF?
A wild-assed guess would be "surely not".
Proof: How could it be? QED.
Proof: It's true for families of _finite_ subsets of N,
but not all sets are finite. QED.
There may be a few details missing in those proofs...
>Keith Ramsay
************************
David C. Ullrich
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