Science Forums
User Name
Password
Science Social Network
home    members    help/rules    who is online    contact   

Go Back   Science Forums > Physical Sciences Forums > Alternative theories
Become a science forums sponsor today
Reply
 
LinkBack Thread Tools
Old 07-26-2008   #1 (permalink)
Adib's Avatar
Curious


 
Adib is an unknown quantity at this point
 



An axiom to settle the continuum hypothesis ?

An axiom to settle the continuum hypothesis ?

(Logic Colloquium 2004 contributed abstract)
Paul Cohen used a set of generic reals to prove the consistency of the negation of the continuum hypothesis with other axioms. It is my opinion that such sets do not really exist for a Platonist. My opinion is that the continuum hypothesis is true.

Here is a tentative axiom from me to try to prove it. Axiom : An infinite subset of the power set of N has a bijection either with a countable union of (pair wise disjoint) sets of n elements or with a countable Cartesian products of (pair wise disjoint) sets of n elements.

Mr Andreas Blass proved that this axiom is equivalent to the continuum hypothesis. So, the axiom is consistent with the other usual axioms and independent from them, from the works of Kurt Godel and Paul Cohen, respectively. Mr Andreas Blass used the assumption that the Cartesian product is not the empty set but he did not use the axiom of choice.

The question which remains is : is it a good axiom ? My opinion is that it is realistic for a Platonist. But may be the axiom is not simple enough and may be a simpler one could be found.
Adib Ben Jebara.
Reply With Quote
Reply

Bookmarks

Tags
continuum hypothesis


Currently Active Users Viewing This Thread: 1 (0 members and 1 guests)
 
Thread Tools

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are On
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
A hypothesis about gravity and magnetism ask Physics and Mathematics 4 02-26-2008 07:52 PM
Matter-manifold hypothesis KALSTER Physics and Mathematics 5 02-06-2008 03:26 AM
My biological hypothesis supersport Biology 34 09-18-2006 10:27 PM
The Riemann hypothesis matrixscarface Physics and Mathematics 6 03-04-2005 03:02 PM
Closed Continuum Robust Physics and Mathematics 31 12-25-2004 08:35 AM


All times are GMT -8. The time now is 07:34 AM.

Hypography?

Hypography [n.]: A combination of "hyperlink" and "bibliography" - ie, a list of links to electronic documents. Comparable to discography and bibliography, but not cartography.

We have been online since May 2000, and aim to be the best place to find and share science-related content of all kinds.

Share the love!

Please add more science to your life. Use our RSS feeds on your blog, your portal, or your favorite feedreader!

Powered by vBulletin® Version 3.7.2
Copyright ©2000 - 2008, Jelsoft Enterprises Ltd.
SEO by vBSEO 3.2.0 ©2008, Crawlability, Inc. Copyright © 2000-2008 Hypography
Part of the Hypography - Science for Everyone Network