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  1. Weak and strong versions of Effective Transfinite Recursion.Patrick Uftring - 2023 - Annals of Pure and Applied Logic 174 (4):103232.
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  • Well ordering principles and -statements: A pilot study.Anton Freund - 2021 - Journal of Symbolic Logic 86 (2):709-745.
    In previous work, the author has shown that $\Pi ^1_1$ -induction along $\mathbb N$ is equivalent to a suitable formalization of the statement that every normal function on the ordinals has a fixed point. More precisely, this was proved for a representation of normal functions in terms of Girard’s dilators, which are particularly uniform transformations of well orders. The present paper works on the next type level and considers uniform transformations of dilators, which are called 2-ptykes. We show that $\Pi (...)
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