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 expounded
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DOI 10.1016/s0168-0072(03)00020-4
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References found in this work BETA

Proof-Theoretic Analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
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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Citations of this work BETA

Proof Theory for Theories of Ordinals II: Π3-Reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.

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