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A direct independence proof of Buchholz's Hydra Game on finite labeled trees

Abstract.

We shall give a direct proof of the independence result of a Buchholz style-Hydra Game on labeled finite trees. We shall show that Takeuti-Arai's cut-elimination procedure of \((\Pi^{1}_{1}-CA) + BI\) and of the iterated inductive definition systems can be directly expressed by the reduction rules of Buchholz's Hydra Game. As a direct corollary the independence result of the Hydra Game follows.

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Received: August 23, 1994 / Revised: July 24, 1995 and May 9, 1996

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Hamano, M., Okada , M. A direct independence proof of Buchholz's Hydra Game on finite labeled trees . Arch Math Logic 37, 67–89 (1998). https://doi.org/10.1007/s001530050084

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  • DOI: https://doi.org/10.1007/s001530050084

  • Mathematics Subject Classification: 03F03, 03F05, 03F35