Proof theory for theories of ordinals—I: recursively Mahlo ordinals

Annals of Pure and Applied Logic 122 (1-3):1-85 (2003)
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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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References found in this work

Proof-theoretic analysis of KPM.Michael Rathjen - 1991 - Archive for Mathematical Logic 30 (5-6):377-403.
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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