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  1. Eine ErweiterungT(V′) des Ordinalzahlensystems 58-0158-0158-01(Λ0) von G. Jäger.Kurt Schütte - 1988 - Archive for Mathematical Logic 27 (1):85-99.
    This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V′) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V′) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V′) is provable in a formal system of second order arithmetic with the axiom schema ofΠ 2 1 -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V′).
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  • Collapsing functions based on recursively large ordinals: A well-ordering proof for KPM. [REVIEW]Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (1):35-55.
    It is shown how the strong ordinal notation systems that figure in proof theory and have been previously defined by employing large cardinals, can be developed directly on the basis of their recursively large counterparts. Thereby we provide a completely new approach to well-ordering proofs as will be exemplified by determining the proof-theoretic ordinal of the systemKPM of [R91].
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  • Ordinal diagrams for Π3-reflection.Toshiyasu Arai - 2000 - Journal of Symbolic Logic 65 (3):1375 - 1394.
    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 (...)
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