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Proof theory for theories of ordinals—I: recursively Mahlo ordinals
Annals of Pure and Applied Logic 122 (1-3):1-85 (2003)
Abstract
This paper deals with a proof theory for a theory T22 of recursively Mahlo ordinals in the form of Π2-reflecting on Π2-reflecting ordinals using a subsystem Od of the system O of ordinal diagrams in Arai 353). This paper is the first published one in which a proof-theoretic analysis à la Gentzen–Takeuti of recursively large ordinals is expoundedMy notes
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Citations of this work
Proof theory for theories of ordinals II: Π3-reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.
Analytic combinatorics, proof-theoretic ordinals, and phase transitions for independence results.Andreas Weiermann - 2005 - Annals of Pure and Applied Logic 136 (1):189-218.
Relativized ordinal analysis: The case of Power Kripke–Platek set theory.Michael Rathjen - 2014 - Annals of Pure and Applied Logic 165 (1):316-339.
Wellfoundedness proofs by means of non-monotonic inductive definitions II: first order operators.Toshiyasu Arai - 2010 - Annals of Pure and Applied Logic 162 (2):107-143.
Wellfoundedness proofs by means of non-monotonic inductive definitions I: Π₂⁰-operators.Toshiyasu Arai - 2004 - Journal of Symbolic Logic 69 (3):830-850.
References found in this work
Proof-theoretic analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
Zur Beweistheorie Der Kripke-Platek-Mengenlehre Über Den Natürlichen Zahlen.Gerhard Jäger - 1980 - Archive for Mathematical Logic 22 (3-4):121-139.
Subsystems of set theory and second order number theory.Wolfram Pohlers - 1998 - In Samuel R. Buss (ed.), Handbook of proof theory. New York: Elsevier. pp. 137--209.
Ordinal diagrams for recursively Mahlo universes.Toshiyasu Arai - 2000 - Archive for Mathematical Logic 39 (5):353-391.
A formalization of the theory of ordinal numbers.Gaisi Takeuti - 1965 - Journal of Symbolic Logic 30 (3):295-317.
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