Tree (descriptive set theory): Difference between revisions

Revision as of 16:47, 11 July 2005

Revision as of 17:23, 11 July 2005

Line 5:

:<math><x_0,x_1,\ldots,x_{n-1}>\in T</math>

:and <math>m<n</math>,

and

:<math>m<n</math>,

then

Line 21 ⟶ 19:

:<math>\vec x|n\in T</math>,

where <math>\vec x|n</math> denotes the sequence of the first <math>n</math> elements of <math>\vec x</math>. The set of all branches through <math>T</math> is denoted <math>[T]</math>.

where

:<math>\vec x|n</math>

denotes the sequence of the first <math>n</math> elements of <math>\vec x</math>. The set of all branches through <math>T</math> is denoted

:<math>[T]</math>.

A tree that has no branches is called '''''[[wellfounded]]'''''; a tree with at least one branch is '''''illfounded'''''.