Journal of Symbolic Logic 65 (3):1375 - 1394 (2000)

Abstract
In this paper we introduce a recursive notation system O(Π 3 ) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of Π 3 -reflection. We show that for each $\alpha in O(Π 3 ) a set theory KP Π 3 for Π 3 -reflection proves that the initial segment of O(Π 3 ) determined by α is a well ordering. Proof theoretic study for such theories will be reported in [4]
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DOI 10.2307/2586705
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References found in this work BETA

Proof Theory of Reflection.Michael Rathjen - 1994 - Annals of Pure and Applied Logic 68 (2):181-224.
Derivatives of Normal Functions and $$\Omega $$ Ω -Models.Toshiyasu Arai - 2018 - Archive for Mathematical Logic 57 (5-6):649-664.
Pure Proof Theory Aims, Methods and Results.Wolfram Pohlers - 1996 - Bulletin of Symbolic Logic 2 (2):159-188.
Ein Wohlordnungsbeweis Für Das OrdinalzahlensystemT(J).K. Schütte - 1988 - Archive for Mathematical Logic 27 (1):5-20.

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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.
Proof Theory of Weak Compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
Proof Theory for Theories of Ordinals II:< I> Π_< Sub> 3-Reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1):39-92.

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