Abstract.
In this paper we introduce a recursive notation system \(O(\mu)\) of ordinals. An element of the notation system is called an ordinal diagram following G. Takeuti [25]. The system is designed for proof theoretic study of theories of recursively Mahlo universes. We show that for each \(\alpha<\Omega\) in \(O(\mu)\) KPM proves that the initial segment of \(O(\mu)\) determined by \(\alpha\) is a well ordering. Proof theoretic study for such theories will be reported in [9].
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Received: 13 January, 1998
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Arai, T. Ordinal diagrams for recursively Mahlo universes. Arch Math Logic 39, 353–391 (2000). https://doi.org/10.1007/s001530050153
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DOI: https://doi.org/10.1007/s001530050153