Annals of Pure and Applied Logic 121 (2-3):163-208 (2003)

Abstract
Hilbert proposed the epsilon substitution method as a basis for consistency proofs. Hilbert's Ansatz for finding a solving substitution for any given finite set of transfinite axioms is, starting with the null substitution S0, to correct false values step by step and thereby generate the process S0,S1,… . The problem is to show that the approximating process terminates. After Gentzen's innovation, Ackermann 162) succeeded to prove termination of the process for first order arithmetic. Inspired by G. Mints as an Ariadne's thread we formulate the epsilon substitution method for the theory ID1 of non-iterated inductive definitions for disjunctions of simply universal and existential operators, and give a termination proof of the H-process based on Ackermann 162). The termination proof is based on transfinite induction up to the Howard ordinal
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DOI 10.1016/s0168-0072(02)00112-4
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References found in this work BETA

Epsilon Substitution Method for Theories of Jump Hierarchies.Toshiyasu Arai - 2002 - Archive for Mathematical Logic 41 (2):123-153.
Strong Termination for the Epsilon Substitution Method.Grigori Mints - 1996 - Journal of Symbolic Logic 61 (4):1193-1205.
Zur Widerspruchsfreiheit der Zahlentheorie.Wilhelm Ackermann - 1940 - Journal of Symbolic Logic 5 (3):125-127.

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Citations of this work BETA

The Epsilon Calculus.Jeremy Avigad & Richard Zach - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Center for the Study of Language and Information, Stanford University.
Hilbert's Program Then and Now.Richard Zach - 2007 - In Dale Jacquette (ed.), Philosophy of Logic. Amsterdam: North Holland. pp. 411–447.
Epsilon Substitution for Transfinite Induction.Henry Towsner - 2004 - Archive for Mathematical Logic 44 (4):397-412.
Epsilon Substitution Method for [Image] -FIX.Toshiyasu Arai - 2006 - Journal of Symbolic Logic 71 (4):1155 - 1188.

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