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"This result is possibly the most famous non-trivial example illustrating Gödel's incompleteness theorem."
This claim is false. Godel's theorem was about the incompleteness of arithmetic. Cohen's result is that the much stronger theory ZF cannot proved and that ZFC cannot prove the continum hypothesis. But neither Choice nor CH are formulable in arithemtic. Godel's Incompleteness result showed that there are purely arithemtical claims that cannot be decided by arithmetic. The undecidability of CH by ZFC is no more an example of that than is the fact that a theory of arithmetic cannot prove that pi is transcendental.
I will leave it for a week and if no discussion has been generated by then, I will delete it.
It is possible that I went overboard by putting the factual errors boiler plate up. If so, sorry, I am new and learning the ways of the wiki.
vanden 03:51, 4 Nov 2003 (UTC)
Charles Matthews 09:07, 4 Nov 2003 (UTC)
Charles Matthews 09:42, 10 Mar 2004 (UTC)
Aleph4 21:01, 10 Mar 2004 (UTC)
In reading the quote by Cohen, I find some words that convey no meaning. To say that a set is "incredibly rich" is to say that any person cannot believe how large a quantity of elements are contained in the set. To say that other people may "express themselves more eloquently" is to say that they will use more appropriate force. But, more force will not result in better proof. Neither of these phrases coveys any clear or intelligible information. 64.12.116.74 12:49, 24 April 2006 (UTC)Lestrade
A recent edit lists Paul Cohen as deceased. A quick check of both google and the Stanford math department home page does not show up with any hits. Is there any source for this info? If not then this may be a hoax. Terry 04:29, 25 March 2007 (UTC)
It s not a hoax. An email was circulated on the Stanford dept mailing list a couple hours before the edit. Obviously the person adding it is well informed.
This article was automatically assessed because at least one article was rated and this bot brought all the other ratings up to at least that level. BetacommandBot 00:22, 28 August 2007 (UTC)
Why mention Sarnak and no other students of his? 86.132.221.158 ( talk) 18:47, 21 April 2015 (UTC)
The result of the move request was: moved. Jenks24 ( talk) 15:47, 29 September 2015 (UTC)
– The page was disambiguated way back in 2006 (unilaterally). Below are the Wikipedia article traffic statistics for the entries in the disambiguation page:
It is clear from the numbers itself that the mathematician is clearly the primary topic in a wide margin. It beats its nearest rival by 4x page views. I propose the pages be moved accordingly. Solomon 7968 18:44, 21 September 2015 (UTC)
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There is a serious problem with this page. The photo that appears in the upper right is not of the right Paul Cohen. I am certain of this, as Paul was one of my professors at Stanford. I don't have time to fix this problem right now. Perhaps someone else can take care of it.
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||
|
"This result is possibly the most famous non-trivial example illustrating Gödel's incompleteness theorem."
This claim is false. Godel's theorem was about the incompleteness of arithmetic. Cohen's result is that the much stronger theory ZF cannot proved and that ZFC cannot prove the continum hypothesis. But neither Choice nor CH are formulable in arithemtic. Godel's Incompleteness result showed that there are purely arithemtical claims that cannot be decided by arithmetic. The undecidability of CH by ZFC is no more an example of that than is the fact that a theory of arithmetic cannot prove that pi is transcendental.
I will leave it for a week and if no discussion has been generated by then, I will delete it.
It is possible that I went overboard by putting the factual errors boiler plate up. If so, sorry, I am new and learning the ways of the wiki.
vanden 03:51, 4 Nov 2003 (UTC)
Charles Matthews 09:07, 4 Nov 2003 (UTC)
Charles Matthews 09:42, 10 Mar 2004 (UTC)
Aleph4 21:01, 10 Mar 2004 (UTC)
In reading the quote by Cohen, I find some words that convey no meaning. To say that a set is "incredibly rich" is to say that any person cannot believe how large a quantity of elements are contained in the set. To say that other people may "express themselves more eloquently" is to say that they will use more appropriate force. But, more force will not result in better proof. Neither of these phrases coveys any clear or intelligible information. 64.12.116.74 12:49, 24 April 2006 (UTC)Lestrade
A recent edit lists Paul Cohen as deceased. A quick check of both google and the Stanford math department home page does not show up with any hits. Is there any source for this info? If not then this may be a hoax. Terry 04:29, 25 March 2007 (UTC)
It s not a hoax. An email was circulated on the Stanford dept mailing list a couple hours before the edit. Obviously the person adding it is well informed.
This article was automatically assessed because at least one article was rated and this bot brought all the other ratings up to at least that level. BetacommandBot 00:22, 28 August 2007 (UTC)
Why mention Sarnak and no other students of his? 86.132.221.158 ( talk) 18:47, 21 April 2015 (UTC)
The result of the move request was: moved. Jenks24 ( talk) 15:47, 29 September 2015 (UTC)
– The page was disambiguated way back in 2006 (unilaterally). Below are the Wikipedia article traffic statistics for the entries in the disambiguation page:
It is clear from the numbers itself that the mathematician is clearly the primary topic in a wide margin. It beats its nearest rival by 4x page views. I propose the pages be moved accordingly. Solomon 7968 18:44, 21 September 2015 (UTC)
Hello fellow Wikipedians,
I have just modified one external link on Paul Cohen. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
This message was posted before February 2018.
After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than
regular verification using the archive tool instructions below. Editors
have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the
RfC before doing mass systematic removals. This message is updated dynamically through the template {{
source check}}
(last update: 5 June 2024).
Cheers.— InternetArchiveBot ( Report bug) 20:07, 1 December 2017 (UTC)
There is a serious problem with this page. The photo that appears in the upper right is not of the right Paul Cohen. I am certain of this, as Paul was one of my professors at Stanford. I don't have time to fix this problem right now. Perhaps someone else can take care of it.