Ackermann’s substitution method

Annals of Pure and Applied Logic 142 (1):1-18 (2006)
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Abstract

We aim at a conceptually clear and technically smooth investigation of Ackermann’s substitution method [W. Ackermann, Zur Widerspruchsfreiheit der Zahlentheorie, Math. Ann. 117 162–194]. Our analysis provides a direct classification of the provably recursive functions of , i.e. Peano Arithmetic framed in the ε-calculus

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10.1016/j.apal.2005.09.016

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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.
Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
Herbrand complexity and the epsilon calculus with equality.Kenji Miyamoto & Georg Moser - 2023 - Archive for Mathematical Logic 63 (1):89-118.
Von neumann’s consistency proof.Luca Bellotti - 2016 - Review of Symbolic Logic 9 (3):429-455.

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References found in 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.
Provability algebras and proof-theoretic ordinals, I.Lev D. Beklemishev - 2004 - Annals of Pure and Applied Logic 128 (1-3):103-123.
Zur Widerspruchsfreiheit der Zahlentheorie.Wilhelm Ackermann - 1940 - Journal of Symbolic Logic 5 (3):125-127.

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