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