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Derivatives of normal functions and \(\omega \)-models

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Abstract

In this note the well-ordering principle for the derivative \(\mathsf{g}^{\prime }\) of normal functions \(\mathsf{g}\) on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded \(\omega \)-models of the well-ordering principle for the function \(\mathsf{g}\).

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Authors and Affiliations

  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. Derivatives of normal functions and \(\omega \)-models. Arch. Math. Logic 57, 649–664 (2018). https://doi.org/10.1007/s00153-017-0600-5

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  • DOI: https://doi.org/10.1007/s00153-017-0600-5

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