About: Kirby-Paris hydra   Sponge Permalink

An Entity of Type : dbkwik:resource/4aznwUI91u-_lcyx_rD8kQ==, within Data Space : 134.155.108.49:8890 associated with source dataset(s)

The Kirby-Paris hydra game is a one-player game played on a tree that can last a very large number of turns. It gives rise to a function \( ext{Hydra}(n)\) that eventually dominates all recursive functions which are provably total in Peano arithmetic, and is itself provably total in PA + "\(\varepsilon_0\) is well-ordered." The game is closely related to Beklemishev's worms.

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rdfs:label
  • Kirby-Paris hydra
rdfs:comment
  • The Kirby-Paris hydra game is a one-player game played on a tree that can last a very large number of turns. It gives rise to a function \( ext{Hydra}(n)\) that eventually dominates all recursive functions which are provably total in Peano arithmetic, and is itself provably total in PA + "\(\varepsilon_0\) is well-ordered." The game is closely related to Beklemishev's worms.
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dbkwik:googology/p...iPageUsesTemplate
Author
  • Laurie Kirby & Jeff Paris
Year
  • 1982(xsd:integer)
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  • \
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abstract
  • The Kirby-Paris hydra game is a one-player game played on a tree that can last a very large number of turns. It gives rise to a function \( ext{Hydra}(n)\) that eventually dominates all recursive functions which are provably total in Peano arithmetic, and is itself provably total in PA + "\(\varepsilon_0\) is well-ordered." The game is closely related to Beklemishev's worms.
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