Abstract
Hydra games were introduced by Kirby and Paris, for the formulation of a result which is independent from Peano arithmetic but depends on the transfinite structure of ε 0. Tree ordinals are a well-known simple way to represent countable ordinals. In this paper we study the relation between these concepts; an ordinal less than ε 0 is canonically translated into both a hydra and a tree ordinal term, and the reduction graph of the hydra and the normal form of the term syntactically correspond to each other.
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Isihara, A. (2007). Hydra Games and Tree Ordinals. In: Leivant, D., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2007. Lecture Notes in Computer Science, vol 4576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73445-1_17
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DOI: https://doi.org/10.1007/978-3-540-73445-1_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73443-7
Online ISBN: 978-3-540-73445-1
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