Tree (descriptive set theory): Difference between revisions

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Closing; no consensus for the merge, and the discussion has been stale for over 18 months; see Talk:Tree (descriptive set theory)#Merge With Tree (set theory)
Undid revision 998041846 by Hellacioussatyr (talk) please do not convert properly formatted mathematics markup into junk pseudo-math templates
 
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A '''branch''' through a tree <math>T</math> is an infinite sequence of elements of <math>X</math>, each of whose finite prefixes belongs to <math>T</math>. The set of all branches through <math>T</math> is denoted <math>[T]</math> and called the '''''body''''' of the tree <math>T</math>.
 
A tree that has no branches is called '''''[[wellfounded]]'''''; a tree with at least one branch is '''''illfounded'''''. By [[KönigKőnig's lemma]], a tree on a [[finite set]] with an infinite number of sequences must necessarily be illfounded.
 
===Terminal nodes===