Talk:Kleene–Brouwer order

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated Start-class, Low-priority)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Low Priority
 Field:  Foundations, logic, and set theory

The Kleene-Brouwer order is not only of interest in descriptive set theory. It carries the names of Kleene and Brouwer (and also, sometimes, if I remember correctly, Kolmogorov) and yet the only reference is to Moschovakis. Ideally, both Kleene and Brouwer should be cited, but I do not know where a reference for Brouwer can be found. Kleene gives a classical proof of the well-foundedness theorem that the article says is so important (in Introduction to Metamathematics?). The Kleene-Brouwer order can be defined over trees over any set which carries a partial order (the order does not have to be total).

I once had a professional interest in this order as I was trying to give a constructive proof of well-foundedness, using the well-ordering principle for the set and the well-ordering principle for the tree over . I conjecture that this is equivalent to the fan theorem when the set is N but I never understood this well enough to attempt a proof.

I'm happy to be corrected on any of the above; and I'd dearly love to find someone who understands it enough to correctly formulate and prove the conjecture above.

btw, I'm pretty new to Wikipedia...

Fairflow (talk) 17:12, 17 October 2010 (UTC)

Well, I think the question is, what would you cite Kleene and Brouwer as saying, that Moschovakis doesn't say? We don't generally strain to use sources just because they're closer to the historical origins of something. However, if there's an important point that's left out, but that you can find in Kleene or Brouwer, then by all means add it and cite them. --Trovatore (talk) 04:46, 18 October 2010 (UTC)
Indeed. I added the Moschovakis reference awhile ago because the article had no citations or references and it was the best resource I had on hand that defined the KB ordering. Not to mention it's a pretty nice and canonical descriptive set theory text that people could go to if they wanted to look more into the topic. If you know a better reference, then by all means add it, but for the content currently on the article, Moschovakis is fine. Thanks for fixing the definition by the way. Wgunther (talk) 17:46, 18 October 2010 (UTC)

External links modified[edit]

Hello fellow Wikipedians,

I have just modified one external link on Kleene–Brouwer order. 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.

You may set the |checked=, on this template, to true or failed to let other editors know you reviewed the change. If you find any errors, please use the tools below to fix them or call an editor by setting |needhelp= to your help request.

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

If you are unable to use these tools, you may set |needhelp=<your help request> on this template to request help from an experienced user. Please include details about your problem, to help other editors.

Cheers.—InternetArchiveBot (Report bug) 13:30, 11 December 2017 (UTC)