Finite Trees as Ordinals
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).
KeywordsBinary Tree Initial Segment Tree Function Recursion Equation Fundamental Function
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