Talk:Tree (set theory)

message: Why is this page called infinite tree, when the given definition does not require the tree to be infinite?  A better name might be "Tree (set theory)" or "Rooted tree (graph theory)" -- the latter to distinguish from the existing article "Tree (graph theory)", which refers to trees without distinguished roots.
Once a final name is picked, the link should be placed on "Tree (disambiguation)" as well.--Trovatore 16:15, 11 July 2005 (UTC)
thread_title: Untitled

message: Well, "disputed" might be too strong a word, but that's what the template wants.  I'm concerned that the given definition for "branch" doesn't require it to be downward-closed, which I would think is intuitively a requirement.  Of course I'm more used to descriptive-set-theoretic trees.  Are there any infinitary combinitorists who can weigh in on whether a "branch" is necessarily downward-closed? --Trovatore 23:58, 12 July 2005 (UTC)
thread_title: (Formerly) Disputed

message: The page says
: The height of a tree is the least ordinal α such that any branch has length at most α. If we have an element x of our tree and the well ordered section of the tree smaller than it is order isomorphic to α then we say x has height α.
This is equivalent to the definition in Kunen, but it takes a little thought to be sure of that.  I think I'd prefer the following:
: The height of an element x of a tree T is the ordinal isomorphic to the collection of all elements of T that are less than x in the tree ordering.  The height of a tree is the least ordinal α such that no element of the tree has height α
I'll look at it here and reflect before making the edit in the actual article. --Trovatore 00:58, 14 July 2005 (UTC)
thread_title: Definition of "height"

message: Is there a reason the introduction for the article uses ε instead of \in? This way, the text is very hard to read and understand. Since I'm a newbie here on Wikipedia, I don't know if there is any precendent regarding the use of set membership operator in introductory text, but I would definitely vote for a change.
Avakar 13:43, 7 December 2006 (UTC)
thread_title:  The use of greek ε for set membership 

message: Yes, I hug ALL types of trees.Notorious Tree Hugger Phinneas J. Hippy 01:54, 7 October 2007 (UTC)
thread_title:  Complex math deserves a hug 

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thread_title:  External links modified 

message: Of course, parts of the pages overlap, but the notion of a tree in general set theory bears significance also in other contexts, eg, a definition of weakly compact cardinals. Paolo Lipparini (talk) 23:22, 24 August 2017 (UTC)
thread_title:  Contrary to the merging with Tree_(descriptive_set_theory).