Abstract
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 φΩω(0).
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© 2005 Springer-Verlag Berlin Heidelberg
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Jervell, H.R. (2005). Finite Trees as Ordinals. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_26
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DOI: https://doi.org/10.1007/11494645_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26179-7
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