Trees are a natural representation for countable ordinals. In particular, finite trees provide a convenient notation the predicative ones. Processes that transform trees or terms can often be proved terminating by viewing the tree or the tree representation of the term as an ordinal.
CITATION STYLE
Dershowitz, N. (1993). Trees, ordinals mad termination. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 668 LNCS, pp. 243–250). Springer Verlag. https://doi.org/10.1007/3-540-56610-4_68
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