Finite Trees as Ordinals

  • Herman Ruge Jervell
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3526)


Finite trees are given a well ordering in such a way that there is a 1-1 correspondence between finite trees and an initial segment of the ordinals. The ordinal ε 0 is the supremum of all binary trees. We get the (fixpoint free) n-ary Veblen hierarchy as tree functions and the supremum of all trees is the small Veblen ordinal φΩ ω (0).


Binary Tree Initial Segment Tree Function Recursion Equation Fundamental Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Herman Ruge Jervell
    • 1
  1. 1.Institutt for lingvistiske og nordiske studierUniversitetet i Oslo Henrik Wergelands husOsloNorway

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