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Topic: Set Theory: Should you believe?
Replies: 778   Last Post: Aug 8, 2006 12:02 PM

 Messages: [ Previous | Next ]
 Rupert Posts: 3,810 Registered: 12/6/04
Re: Set Theory: Should you believe?
Posted: Aug 3, 2006 9:22 PM

Virgil wrote:
> In article <e9ulgr\$9b7\$1@nntp.aioe.org>,
> David Bernier <ezcos@yahoo.com> wrote:
>

> > Obviously, one wants ordinals of uncountable order type.
> > In ZC without any additional axioms, it would seem that one
> > can only prove the existence of von Neumann ordinals that are
> > countable (either finite or infinite).
> >
> > So in plain ZC, what would be a good definition of an
> > ordinal?

>
> Is there any reason why one cannot use the same definition as in ZF and
> NBG?
>

It doesn't work very well because you don't have the axiom of
replacement, so you can't prove that omega times two exists as usually
defined when we're working in ZF. It's better to define an ordinal to
be a set which is equal to the set of all well-ordered sets of minimal
rank order isomorphic to a given well-ordered set. You get more
ordinals that way.

> The von Neumann definition of NBG is :
> A set S is an ordinal if and only if S is totally ordered with respect
> to set containment and every element of S is also a subset of S.

Date Subject Author
7/12/06 Norman Wildberger
7/12/06 malbrain@yahoo.com
7/12/06 Peter Webb
7/12/06 lesterzick@cableone.net
7/12/06 Virgil
7/13/06 lesterzick@cableone.net
7/13/06 Hatto von Aquitanien
7/13/06 Aatu Koskensilta
7/13/06 stephen@nomail.com
7/13/06 Hatto von Aquitanien
7/13/06 Hatto von Aquitanien
7/14/06 David C. Ullrich
7/14/06 Hatto von Aquitanien
7/14/06 Peter Webb
7/15/06 David C. Ullrich
7/15/06 DontBother@nowhere.net
7/16/06 David C. Ullrich
7/16/06 DontBother@nowhere.net
7/14/06 George Greene
7/14/06 Hatto von Aquitanien
7/13/06 Dave L. Renfro
7/14/06 Shmuel (Seymour J.) Metz
7/14/06 DontBother@nowhere.net
7/15/06 Virgil
7/15/06 DontBother@nowhere.net
7/15/06 Virgil
7/15/06 DontBother@nowhere.net
7/16/06 Virgil
7/16/06 DontBother@nowhere.net
7/17/06 Jack Markan
7/17/06 DontBother@nowhere.net
7/18/06 Chas Brown
7/18/06 DontBother@nowhere.net
7/18/06 Jack Markan
7/18/06 Jack Markan
7/19/06 DontBother@nowhere.net
7/19/06 Jack Markan
7/19/06 DontBother@nowhere.net
7/19/06 Jack Markan
7/19/06 DontBother@nowhere.net
7/18/06 DontBother@nowhere.net
7/18/06 Jack Markan
7/19/06 DontBother@nowhere.net
7/19/06 Chris Menzel
7/19/06 DontBother@nowhere.net
7/19/06 Jack Markan
7/19/06 DontBother@nowhere.net
7/19/06 Jack Markan
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/20/06 DontBother@nowhere.net
7/20/06 Virgil
7/20/06 DontBother@nowhere.net
7/20/06 Virgil
7/21/06 DontBother@nowhere.net
7/21/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Patricia Shanahan
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/22/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Dr. David Kirkby
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/18/06 Richard Herring
7/18/06 DontBother@nowhere.net
7/13/06 Gerry Myerson
7/13/06 Gene Ward Smith
7/13/06 Gerry Myerson
7/13/06 Gene Ward Smith
7/13/06 Lee Rudolph
7/13/06 Aatu Koskensilta
7/13/06 Gerry Myerson
7/13/06 Stephen Montgomery-Smith
7/13/06 Mariano
7/13/06 Stephen Montgomery-Smith
7/14/06 Mariano
7/14/06 Stephen Montgomery-Smith
7/14/06 Mariano
7/14/06 Stephen Montgomery-Smith
7/14/06 DontBother@nowhere.net
7/18/06 Rupert
7/18/06 DontBother@nowhere.net
7/18/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/20/06 Y. T.
7/20/06 Virgil
7/24/06 Y. T.
7/24/06 Virgil
7/22/06 Shmuel (Seymour J.) Metz
7/24/06 Y. T.
7/24/06 Virgil
7/26/06 Y. T.
7/26/06 Virgil
7/30/06 Y. T.
7/26/06 Shmuel (Seymour J.) Metz
7/30/06 Y. T.
7/18/06 Rupert
7/19/06 DontBother@nowhere.net
7/23/06 Rupert
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/24/06 Rupert
7/24/06 DontBother@nowhere.net
7/27/06 Rupert
7/27/06 DontBother@nowhere.net
7/28/06 Rupert
7/29/06 DontBother@nowhere.net
7/29/06 Rupert
7/30/06 DontBother@nowhere.net
7/30/06 Rupert
7/30/06 DontBother@nowhere.net
7/31/06 Rupert
7/31/06 DontBother@nowhere.net
8/4/06 DontBother@nowhere.net
8/4/06 Rupert
8/6/06 DontBother@nowhere.net
8/7/06 Rupert
8/8/06 DontBother@nowhere.net
7/28/06 Chris Menzel
7/28/06 Aatu Koskensilta
7/29/06 DontBother@nowhere.net
7/29/06 Aatu Koskensilta
7/29/06 DontBother@nowhere.net
7/29/06 Aatu Koskensilta
7/29/06 DontBother@nowhere.net
7/29/06 Aatu Koskensilta
7/30/06 DontBother@nowhere.net
8/1/06 Aatu Koskensilta
8/2/06 DontBother@nowhere.net
7/30/06 Ross Finlayson
8/1/06 Aatu Koskensilta
8/1/06 George Greene
7/29/06 Virgil
7/29/06 DontBother@nowhere.net
7/29/06 DontBother@nowhere.net
7/29/06 Chris Menzel
7/29/06 Aatu Koskensilta
7/29/06 Chris Menzel
7/30/06 DontBother@nowhere.net
7/29/06 DontBother@nowhere.net
7/29/06 DontBother@nowhere.net
7/13/06 DontBother@nowhere.net
7/13/06 DontBother@nowhere.net
7/13/06 Gene Ward Smith
7/13/06 Stephen Montgomery-Smith
7/14/06 Daryl McCullough
7/14/06 Peter Webb
7/14/06 Stephen Montgomery-Smith
7/14/06 DontBother@nowhere.net
7/14/06 Shmuel (Seymour J.) Metz
7/14/06 dkfjdklj@yahoo.com
7/14/06 Gene Ward Smith
7/14/06 dkfjdklj@yahoo.com
7/14/06 Rupert
7/14/06 guenther.vonKnakspott@gmx.de
7/14/06 Stephen Montgomery-Smith
7/14/06 Hatto von Aquitanien
7/14/06 Barb Knox
7/14/06 Hatto von Aquitanien
7/14/06 Barb Knox
7/14/06 Hatto von Aquitanien
7/14/06 Gene Ward Smith
7/14/06 Hatto von Aquitanien
7/14/06 Virgil
7/15/06 Gene Ward Smith
7/15/06 Hatto von Aquitanien
7/15/06 Dave Seaman
7/14/06 Patricia Shanahan
7/14/06 Hatto von Aquitanien
7/14/06 Stephen Montgomery-Smith
7/15/06 Virgil
7/15/06 Stephen Montgomery-Smith
7/15/06 DontBother@nowhere.net
7/15/06 Patricia Shanahan
7/15/06 DontBother@nowhere.net
7/15/06 Virgil
7/15/06 DontBother@nowhere.net
7/15/06 Virgil
7/15/06 Dr. David Kirkby
7/16/06 DontBother@nowhere.net
7/16/06 DontBother@nowhere.net
7/20/06 Rupert
7/17/06 Aatu Koskensilta
7/17/06 dkfjdklj@yahoo.com
7/17/06 Aatu Koskensilta
7/14/06 R. Srinivasan
7/14/06 Kevin Karn
7/15/06 Dave L. Renfro
7/15/06 R. Srinivasan
7/15/06 Kevin Karn
7/15/06 R. Srinivasan
7/15/06 stephen@nomail.com
7/15/06 R. Srinivasan
7/15/06 Patricia Shanahan
7/15/06 Daryl McCullough
7/15/06 Patricia Shanahan
7/15/06 Peter Webb
7/15/06 R. Srinivasan
7/17/06 Kevin Karn
7/17/06 Patricia Shanahan
7/17/06 dkfjdklj@yahoo.com
7/17/06 Patricia Shanahan
7/17/06 dkfjdklj@yahoo.com
7/17/06 malbrain@yahoo.com
7/17/06 Patricia Shanahan
7/17/06 malbrain@yahoo.com
7/17/06 Chas Brown
7/17/06 malbrain@yahoo.com
7/17/06 Chas Brown
7/17/06 malbrain@yahoo.com
7/17/06 DontBother@nowhere.net
7/17/06 malbrain@yahoo.com
7/17/06 DontBother@nowhere.net
7/18/06 malbrain@yahoo.com
7/19/06 DontBother@nowhere.net
7/17/06 Virgil
7/17/06 DontBother@nowhere.net
7/18/06 Virgil
7/18/06 DontBother@nowhere.net
7/17/06 Chas Brown
7/18/06 Aatu Koskensilta
7/18/06 DontBother@nowhere.net
7/18/06 Chas Brown
7/18/06 Gerry Myerson
7/19/06 Chas Brown
7/19/06 Gerry Myerson
7/19/06 Chas Brown
7/20/06 Shmuel (Seymour J.) Metz
7/19/06 Aatu Koskensilta
7/19/06 Chas Brown
7/20/06 Shmuel (Seymour J.) Metz
7/20/06 Aatu Koskensilta
7/20/06 Lee Rudolph
7/20/06 Aatu Koskensilta
7/20/06 David Bernier
7/21/06 Aatu Koskensilta
7/21/06 George Greene
7/18/06 malbrain@yahoo.com
7/18/06 DontBother@nowhere.net
7/18/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/18/06 malbrain@yahoo.com
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/17/06 Russell Easterly
7/17/06 jirka@5z.com
7/17/06 malbrain@yahoo.com
7/17/06 jirka@5z.com
7/17/06 malbrain@yahoo.com
7/17/06 Patricia Shanahan
7/17/06 malbrain@yahoo.com
7/17/06 DontBother@nowhere.net
7/17/06 Virgil
7/18/06 namducnguyen
7/18/06 DontBother@nowhere.net
7/18/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/20/06 DontBother@nowhere.net
7/20/06 Virgil
7/20/06 DontBother@nowhere.net
7/18/06 namducnguyen
7/18/06 namducnguyen
7/18/06 DontBother@nowhere.net
7/18/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/20/06 DontBother@nowhere.net
7/20/06 Virgil
7/20/06 DontBother@nowhere.net
7/18/06 namducnguyen
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/19/06 DontBother@nowhere.net
7/19/06 Virgil
7/20/06 DontBother@nowhere.net
7/20/06 Virgil
7/20/06 DontBother@nowhere.net
7/20/06 Virgil
7/21/06 DontBother@nowhere.net
7/21/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 Jan Burse
7/24/06 Virgil
7/24/06 DontBother@nowhere.net
7/24/06 DontBother@nowhere.net
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/18/06 Rupert
7/18/06 namducnguyen
7/19/06 Rupert
7/20/06 namducnguyen
7/20/06 DontBother@nowhere.net
7/20/06 namducnguyen
7/21/06 DontBother@nowhere.net
7/21/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/22/06 DontBother@nowhere.net
7/27/06 Rupert
7/27/06 DontBother@nowhere.net
7/28/06 Rupert
7/29/06 DontBother@nowhere.net
7/29/06 Virgil
7/29/06 DontBother@nowhere.net
7/29/06 Virgil
7/30/06 DontBother@nowhere.net
7/30/06 Virgil
7/30/06 DontBother@nowhere.net
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7/29/06 namducnguyen
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7/19/06 namducnguyen
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7/20/06 Rupert
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7/20/06 Virgil
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7/20/06 Virgil
7/21/06 DontBother@nowhere.net
7/21/06 Virgil
7/21/06 DontBother@nowhere.net
7/21/06 Virgil
7/22/06 herbzet@cox.net
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7/23/06 herbzet@cox.net
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7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/24/06 DontBother@nowhere.net
7/22/06 herbzet@cox.net
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7/22/06 Virgil
7/22/06 DontBother@nowhere.net
7/22/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
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7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/23/06 herbzet@cox.net
7/23/06 herbzet@cox.net
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/23/06 herbzet@cox.net
7/24/06 DontBother@nowhere.net
7/24/06 herbzet@cox.net
7/24/06 DontBother@nowhere.net
7/24/06 herbzet@cox.net
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7/28/06 herbzet@cox.net
7/29/06 DontBother@nowhere.net
7/30/06 herbzet@cox.net
7/30/06 DontBother@nowhere.net
7/24/06 Virgil
7/24/06 Virgil
7/23/06 herbzet@cox.net
7/22/06 herbzet@cox.net
7/22/06 Virgil
7/22/06 herbzet@cox.net
7/20/06 Rupert
7/21/06 namducnguyen
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7/31/06 namducnguyen
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7/21/06 Virgil
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7/21/06 Virgil
7/21/06 Dr. David Kirkby
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7/22/06 DontBother@nowhere.net
7/22/06 Virgil
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7/19/06 Virgil
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7/20/06 Virgil
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7/20/06 Virgil
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7/21/06 jirka@5z.com
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7/23/06 jirka@5z.com
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7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/23/06 Aatu Koskensilta
7/23/06 Dr. David Kirkby
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
7/23/06 DontBother@nowhere.net
7/23/06 Virgil
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7/23/06 Virgil
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/24/06 R. Srinivasan
7/24/06 DontBother@nowhere.net
7/24/06 Virgil
7/23/06 jirka@5z.com
7/23/06 DontBother@nowhere.net
7/24/06 Aatu Koskensilta
7/24/06 DontBother@nowhere.net
7/25/06 Gc
7/25/06 Aatu Koskensilta
7/25/06 Gc
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7/25/06 Gc
7/25/06 Gc
7/25/06 Chris Menzel
7/25/06 Gc
7/26/06 Chris Menzel
7/26/06 Gc
7/28/06 George Greene
7/28/06 Aatu Koskensilta
7/25/06 Pierre Asselin
7/25/06 Dr. David Kirkby
7/26/06 DontBother@nowhere.net
7/26/06 DontBother@nowhere.net
7/26/06 Pierre Asselin
7/27/06 DontBother@nowhere.net
7/26/06 jirka@5z.com
7/26/06 Gc
7/24/06 Aatu Koskensilta
7/24/06 jirka@5z.com
7/24/06 Aatu Koskensilta
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7/25/06 Aatu Koskensilta
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7/22/06 Patricia Shanahan
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7/24/06 Virgil
7/18/06 Aatu Koskensilta
7/18/06 DontBother@nowhere.net
7/19/06 David Bernier
7/19/06 Aatu Koskensilta
7/22/06 Keith Ramsay
7/22/06 David Bernier
7/22/06 Virgil
8/3/06 Rupert
7/17/06 Toni Lassila
7/14/06 Phil Carmody
7/14/06 Stephen Montgomery-Smith
7/20/06 Y. T.
7/13/06 Peter Webb
7/13/06 Gerry Myerson
7/13/06 Stephen Montgomery-Smith
7/14/06 Kevin Karn
7/14/06 Gene Ward Smith
7/15/06 Stephen Montgomery-Smith
7/15/06 Stephen Montgomery-Smith
7/15/06 Gene Ward Smith
7/15/06 Hatto von Aquitanien
7/15/06 Stephen Montgomery-Smith
7/15/06 Barb Knox
7/15/06 Daryl McCullough
7/15/06 Peter Webb
7/15/06 Chas Brown
7/15/06 T.H. Ray
7/15/06 DontBother@nowhere.net
7/15/06 Lee Rudolph
7/17/06 James Dolan
7/14/06 Peter Webb
7/17/06 Rupert
7/13/06 Russell Easterly
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7/13/06 Gene Ward Smith
7/13/06 Hatto von Aquitanien
7/13/06 Stephen Montgomery-Smith
7/14/06 Hatto von Aquitanien
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7/13/06 Hatto von Aquitanien
7/13/06 DontBother@nowhere.net
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7/15/06 Virgil
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7/13/06 Peter Webb
7/13/06 Gene Ward Smith
7/13/06 Gerry Myerson
7/13/06 Gene Ward Smith
7/14/06 R. Srinivasan
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7/14/06 DontBother@nowhere.net
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7/14/06 Hatto von Aquitanien
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7/14/06 DontBother@nowhere.net
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7/15/06 Virgil
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7/16/06 Virgil
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7/18/06 Rupert
7/19/06 DontBother@nowhere.net
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7/19/06 Virgil
7/20/06 Dave L. Renfro
7/20/06 Dave L. Renfro
7/20/06 DontBother@nowhere.net
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7/24/06 Rupert
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7/14/06 George Greene
7/14/06 George Greene
7/14/06 George Greene
7/14/06 Rupert
7/14/06 George Greene
7/14/06 T.H. Ray
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7/12/06 David Petry
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7/13/06 Gene Ward Smith
7/14/06 Gerry Myerson
7/14/06 Gene Ward Smith
7/14/06 Gerry Myerson
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7/13/06 guenther.vonKnakspott@gmx.de
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7/14/06 Hatto von Aquitanien
7/14/06 Stephen Montgomery-Smith
7/14/06 Hatto von Aquitanien
7/14/06 Stephen Montgomery-Smith
7/14/06 Stephen Montgomery-Smith
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8/3/06 Anonymous