Journal of Symbolic Logic 71 (4):1155 - 1188 (2006)

Abstract
In this paper we formulate epsilon substitution method for a theory $\Pi _{2}^{0}$-FIX for non-monotonic $\Pi _{2}^{0}$ inductive definitions. Then we give a termination proof of the H-processes based on Ackermann [1]
Keywords Epsilon substitution  Ordinal interpretation  Termination proof
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DOI 10.2178/jsl/1164060450
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References found in this work BETA

Epsilon Substitution Method for ID1.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 121 (2-3):163-208.
Proof Theory for Theories of Ordinals II: Π3-Reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.
Epsilon Substitution Method for Theories of Jump Hierarchies.Toshiyasu Arai - 2002 - Archive for Mathematical Logic 41 (2):123-153.
Epsilon Substitution for Transfinite Induction.Henry Towsner - 2004 - Archive for Mathematical Logic 44 (4):397-412.
Epsilon Substitution Method for [Π0 1, Π0 1]-FIX.T. Arai - 2005 - Archive for Mathematical Logic 44 (8):1009-1043.

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Citations of this work BETA

Proof Theory of Weak Compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
A Sneak Preview of Proof Theory of Ordinals.Toshiyasu Arai - 2012 - Annals of the Japan Association for Philosophy of Science 20:29-47.
Epsilon Substitution for $$\Textit{ID}_1$$ ID 1 Via Cut-Elimination.Henry Towsner - 2018 - Archive for Mathematical Logic 57 (5-6):497-531.
Exact Bounds on Epsilon Processes.Toshiyasu Arai - 2011 - Archive for Mathematical Logic 50 (3-4):445-458.

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