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Topic: Joel David Hamkins on definable real numbers in analysis
Replies: 98   Last Post: Jun 30, 2013 3:22 PM

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 Peter Percival Posts: 2,623 Registered: 10/25/10
Re: Joel David Hamkins on definable real numbers in analysis
Posted: Jun 19, 2013 8:12 AM

mueckenh@rz.fh-augsburg.de wrote:

>
> Look: Zermelo has "proved" that the real numbers can be well-ordered. But it has been proved that the real numbers in fact cannot be well-ordered. That is as certain as that you cannot get a 13 with two dice.

I think you're confusing two different results. There are models of ZFC
in which a well-ordering is a not definable. That does not mean that R
cannot be well ordered, it just means that if phi(x,y) is the ordering
relation, phi is not a formula of ZFC.

--
I think I am an Elephant,
Behind another Elephant
Behind /another/ Elephant who isn't really there....
A.A. Milne

Date Subject Author
6/18/13 fom
6/19/13 David Petry
6/19/13 fom
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Peter Percival
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Virgil
6/19/13 Tucsondrew@me.com
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6/21/13 Virgil
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6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Tucsondrew@me.com
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6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/25/13 Virgil
6/25/13 Virgil
6/26/13 Virgil
6/26/13 fom
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6/22/13 Virgil
6/22/13 Tucsondrew@me.com
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/22/13 David C. Ullrich
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/23/13 David C. Ullrich
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6/24/13 David C. Ullrich
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
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6/25/13 mueckenh@rz.fh-augsburg.de
6/25/13 Virgil
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/25/13 Tucsondrew@me.com
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/26/13 David C. Ullrich
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
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6/26/13 Virgil
6/27/13 mueckenh@rz.fh-augsburg.de
6/27/13 Virgil
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6/29/13 mueckenh@rz.fh-augsburg.de
6/29/13 Virgil
6/30/13 Virgil
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6/29/13 Virgil
6/28/13 Virgil
6/28/13 Virgil
6/19/13 Virgil
6/19/13 Virgil