Ideas in the epsilon substitution method for -FIX

Annals of Pure and Applied Logic 136 (1-2):3-21 (2005)

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 [W. Ackermann, Zur Widerspruchsfreiheit der Zahlentheorie, Math. Ann. 117 162–194] succeeded in proving the termination of the process for the first order arithmetic. In this note we report recent progress on the subject, and expound basic ideas of the epsilon substitution method à la Ackermann for the theory -FIX of non-monotonic inductive definitions.
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DOI 10.1016/j.apal.2005.05.004
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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.
Epsilon Substitution Method for Theories of Jump Hierarchies.Toshiyasu Arai - 2002 - Archive for Mathematical Logic 41 (2):123-153.
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.
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Exact Bounds on Epsilon Processes.Toshiyasu Arai - 2011 - Archive for Mathematical Logic 50 (3-4):445-458.

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