How strong are single fixed points of normal functions?

Journal of Symbolic Logic 85 (2):709-732 (2020)
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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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10.1017/jsl.2020.24

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Citations of this work

Derivatives of normal functions in reverse mathematics.Anton Freund & Michael Rathjen - 2021 - Annals of Pure and Applied Logic 172 (2):102890.

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References found in this work

Reverse mathematics and ordinal exponentiation.Jeffry L. Hirst - 1994 - Annals of Pure and Applied Logic 66 (1):1-18.
Computable aspects of the Bachmann–Howard principle.Anton Freund - 2019 - Journal of Mathematical Logic 20 (2):2050006.

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