Hydra Games and Tree Ordinals
Akira Ishihara · Data Archiving and Networked Services (DANS) · 2007
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 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 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.