In mathematics, especially mathematical logic, graph theory and number theory, the Buchholz hydra game is a type of hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree. The hydra game can be used to generate a rapidly growing function, , which eventually dominates all recursive functions that are provably total in "", and the termination of all hydra games is not provably total in .[1]
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the Buchholzhydra game is a type of hydra game, which is a single-player game based on the idea of chopping pieces off a mathematical tree. The hydra game...
fast-growing hierarchy. This is not the most powerful hydra. The Buchholzhydra is a more potent hydra. It entails a labelled tree. The root has a unique...
Buchholz (surname) Buchholzhydra, a mathematical game on a labeled tree Buchholz psi functions, a system of ordinal collapsing functions Buchholz's ID...
the hydras from Buchholz'shydra game are isomorphic to Buchholz's ordinal notation, the ordinals up to this point can be expressed using hydras from...
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Cambridge University Press. p. 53. ISBN 0-521-77136-6. OCLC 43561897. Buchholz, Elke Linda. Francisco de Goya. Cologne: Könemann, 1999. ISBN 3-8290-2930-6...
introduced by Buchholz but is limited to collapsing one cardinal for clarity of exposition. More on the relation between this example and Buchholz's system will...
PhD Dissertation, University of Texas at Arlington. ISBN 0496859366. Buchholz & Fiedler 1987, p. 28-31. Granser, Thedor; Moosmüller, Sylvia. "The schwa...
order isomorphic to ε0. This representation is related to the proof of the hydra theorem, which represents decreasing sequences of ordinals as a graph-theoretic...
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