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arXiv · 2302.08874

Metric fixed point theory and partial impredicativity

David Fernández-Duque·Paul Shafer·Henry Towsner·Keita Yokoyama
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Abstract

We show that the Priess-Crampe & Ribenboim fixed point theorem is provable in $\mathsf{RCA}_0$. Furthermore, we show that Caristi's fixed point theorem for both Baire and Borel functions is equivalent to the transfinite leftmost path principle, which falls strictly between $\mathsf{ATR}_0$ and $\Pi^1_1\mbox{-}\mathsf{CA}_0$. We also exhibit several weakenings of Caristi's theorem that are equivalent to $\mathsf{WKL}_0$ and to $\mathsf{ACA}_0$.

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BibTeXRIS

David Fernández-Duque, Paul Shafer, Henry Towsner, Keita Yokoyama. 2023-02-17. Metric fixed point theory and partial impredicativity. https://arxiv.org/abs/2302.08874

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