Loebl, Martin Hercules and Hydra. (English) Zbl 0666.05024 Commentat. Math. Univ. Carol. 29, No. 1, 85-95 (1988). Hercules and Hydra is a game on finite rooted trees. In what follows, it is supposed that the game starts with a path \(T_ 0\) and the sequence of rooted trees \(T_ 0,T_ 1,T_ 2,..\). (resulting in course of the game) is called a trajectory. The author defines two simple recursive strategies MAX, MIN of Hercules. He proves that they give trajectories of maximum and minimum length, respectively. Improving a result of L. Kirby and J. Paris [Bull. Lond. Math. Soc. 14, 285-293 (1982; Zbl 0501.03017)], he shows that the statement “Strategy MAX is a winning strategy of Hercules” cannot be proved in Peano arithmetic. Reviewer: A.Ádám MSC: 05C05 Trees 91A99 Game theory 03B25 Decidability of theories and sets of sentences Keywords:game; rooted trees Citations:Zbl 0501.03017 PDF BibTeX XML Cite \textit{M. Loebl}, Commentat. Math. Univ. Carol. 29, No. 1, 85--95 (1988; Zbl 0666.05024) Full Text: EuDML OpenURL