Update Procedures and the 1-Consistency of Arithmetic

Mathematical Logic Quarterly 48 (1):3-13 (2002)
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Abstract

The 1-consistency of arithmetic is shown to be equivalent to the existence of fixed points of a certain type of update procedure, which is implicit in the epsilon-substitution method

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Jeremy Avigad
Carnegie Mellon University

Citations of this work

The Epsilon Calculus.Jeremy Avigad & Richard Zach - 2014 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. Stanford, CA: The Metaphysics Research Lab.
Ackermann’s substitution method.Georg Moser - 2006 - Annals of Pure and Applied Logic 142 (1):1-18.
A constructive analysis of learning in Peano Arithmetic.Federico Aschieri - 2012 - Annals of Pure and Applied Logic 163 (11):1448-1470.

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References found in this work

Elementary descent recursion and proof theory.Harvey Friedman & Michael Sheard - 1995 - Annals of Pure and Applied Logic 71 (1):1-45.
The substitution method.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):175-192.
Functionals defined by transfinite recursion.W. W. Tait - 1965 - Journal of Symbolic Logic 30 (2):155-174.
Strong termination for the epsilon substitution method.Grigori Mints - 1996 - Journal of Symbolic Logic 61 (4):1193-1205.

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