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HOW STRONG ARE SINGLE FIXED POINTS OF NORMAL FUNCTIONS?
Published online by Cambridge University Press: 20 July 2020
Abstract
In a recent paper by M. Rathjen and the present author it has been shown that the statement “every normal function has a derivative” is equivalent to $\Pi ^1_1$ -bar induction. The equivalence was proved over $\mathbf {ACA_0}$ , for a suitable representation of normal functions in terms of dilators. In the present paper, we show that the statement “every normal function has at least one fixed point” is equivalent to $\Pi ^1_1$ -induction along the natural numbers.
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- © The Association for Symbolic Logic 2020
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