Re: Hausdorff antimaximality principle
- From: David C. Ullrich <ullrich@xxxxxxxxxxxxxxxx>
- Date: Mon, 15 Jan 2007 08:42:31 -0600
On Sun, 14 Jan 2007 12:54:54 -0500, "G. A. Edgar"
<edgar@xxxxxxxxxxxxxxxxxxxxxxxxxxx> wrote:
In article <819kq2l0c000c8jp1r113ab6jef8lr0e2t@xxxxxxx>, David C.
Ullrich <ullrich@xxxxxxxxxxxxxxxx> wrote:
On Sun, 14 Jan 2007 03:02:27 -0800, William Elliot
<marsh@xxxxxxxxxxxxxxxxxx> wrote:
Hausdorff maximality theorem, HM.
Every (partially) ordered set contains a maximal chain.
HM is equivalent to Zorn's lemma, AxC, etc.
A quick result of Zorn's lemma is
every (partially) ordered set contains a maximal antichain.
Does this maximal antichain principle imply Zorn's lemma, AxC, etc.
If so which would be the easier to prove from maximal antichain?
If R is a partial order and S is the reverse of R, defined by
xSy if and only if yRx, then S is also a partial order.
But reversed chains are still chains, not antichains.
Yeah, I realized what I'd screwed up in the interval
between seeing you'd replied and seeing the reply...
Never mind.
************************
David C. Ullrich
.
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