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Epsilon substitution method for theories of jump hierarchies

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Abstract.

 We formulate epsilon substitution method for theories (H)α0 of absolute jump hierarchies, and give two termination proofs of the H-process: The first proof is an adaption of Mints M, Mints-Tupailo-Buchholz MTB, i.e., based on a cut-elimination of a specially devised infinitary calculus. The second one is an adaption of Ackermann Ack. Each termination proof is based on transfinite induction up to an ordinal θ(α0+ ω)0, which is best possible.

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  1. Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521 Japan. e-mail: arai@mis.hiroshima-u.ac.jp, , , , , , JP

    Toshiyasu Arai

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  1. Toshiyasu Arai
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Received: 19 April 1999 / Published online: 20 December 2001

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Arai, T. Epsilon substitution method for theories of jump hierarchies. Arch. Math. Logic 41, 123–153 (2002). https://doi.org/10.1007/s001530100108

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  • DOI: https://doi.org/10.1007/s001530100108

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