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Updated: Aug 3, 2025

An Operant Intra-/Extra-dimensional Set-shift Task for Mice
Published on: January 22, 2016
Metric fixed point theory and partial impredicativity
D Fernández-Duque1,2, P Shafer3, H Towsner4
1Department of Mathematics WE16, Ghent University, Ghent, Belgium.
Abstract:
We show that the Priess-Crampe & Ribenboim fixed point theorem is provable in [Formula: see text]. 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 [Formula: see text] and [Formula: see text]. We also exhibit several weakenings of Caristi's theorem that are equivalent to [Formula: see text] and to [Formula: see text]. This article is part of the theme issue 'Modern perspectives in Proof Theory'.
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