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Proof-theoretic strengths of the well-ordering principles

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Abstract

In this note the proof-theoretic ordinal of the well-ordering principle for the normal functions \(\mathsf {g}\) on ordinals is shown to be equal to the least fixed point of \(\mathsf {g}\). Moreover corrections to the previous paper (Arai in Arch Math Log 57:649–664, 2017) are made.

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Acknowledgements

I’d like to thank A. Freund for pointing out a flaw in [3], and the anonymous referee for a careful reading and helpful suggestions.

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  1. Toshiyasu Arai

    Present address: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan

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  1. Graduate School of Science, Chiba University, 1-33, Yayoi-cho, Inage-ku, Chiba, 263-8522, Japan

    Toshiyasu Arai

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  1. Toshiyasu Arai
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Correspondence to Toshiyasu Arai.

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Arai, T. Proof-theoretic strengths of the well-ordering principles. Arch. Math. Logic 59, 257–275 (2020). https://doi.org/10.1007/s00153-019-00689-4

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  • DOI: https://doi.org/10.1007/s00153-019-00689-4

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