Epsilon substitution method for theories of jump hierarchies

Archive for Mathematical Logic 41 (2):123-153 (2002)
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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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10.1007/s001530100108

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Citations of this work

Epsilon substitution method for ID1.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 121 (2-3):163-208.
Cut elimination for a simple formulation of epsilon calculus.Grigori Mints - 2008 - Annals of Pure and Applied Logic 152 (1):148-160.
Ackermann’s substitution method.Georg Moser - 2006 - Annals of Pure and Applied Logic 142 (1):1-18.
Ideas in the epsilon substitution method for -FIX.Toshiyasu Arai - 2005 - Annals of Pure and Applied Logic 136 (1-2):3-21.
Epsilon Substitution Method for [image] -FIX.Toshiyasu Arai - 2006 - Journal of Symbolic Logic 71 (4):1155 - 1188.

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References found in this work

A new system of proof-theoretic ordinal functions.W. Buchholz - 1986 - Annals of Pure and Applied Logic 32:195-207.
A survey of mathematical logic.Hao Wang - 1963 - Amsterdam: North-Holland Publishing Company.
A Survey of Mathematical Logic.Hao Wang - 1965 - Journal of Symbolic Logic 30 (2):249-250.

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