Epsilon Substitution Method for [image] -FIX

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

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DOI

10.2178/jsl/1164060450

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original Arai, Toshiyasu (2003) "Epsilon substitution method for ID1". Annals of Pure and Applied Logic 121(2):163-208
reprint Arai, T. (2005) "Epsilon substitution method for [Π0 1, Π0 1]-FIX". Archive for Mathematical Logic 44(8):1009-1043

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Citations of this work

Proof theory of weak compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
Epsilon substitution for $$\textit{ID}_1$$ ID 1 via cut-elimination.Henry Towsner - 2018 - Archive for Mathematical Logic 57 (5-6):497-531.
A Sneak Preview of Proof Theory of Ordinals.Toshiyasu Arai - 2012 - Annals of the Japan Association for Philosophy of Science 20:29-47.
Exact bounds on epsilon processes.Toshiyasu Arai - 2011 - Archive for Mathematical Logic 50 (3-4):445-458.

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References found in this work

Epsilon substitution method for ID1.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 121 (2):163-208.
Epsilon substitution method for theories of jump hierarchies.Toshiyasu Arai - 2002 - Archive for Mathematical Logic 41 (2):123-153.
Proof theory for theories of ordinals II: Π3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1):39-92.
Epsilon substitution for transfinite induction.Henry Towsner - 2005 - Archive for Mathematical Logic 44 (4):397-412.

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