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HOW STRONG ARE SINGLE FIXED POINTS OF NORMAL FUNCTIONS?

Published online by Cambridge University Press:  20 July 2020

ANTON FREUND*
Affiliation:
FACHBEREICH MATHEMATIK TECHNISCHE UNIVERSITÄT DARMSTADT SCHLOSSGARTENSTRASSE 7, 64289DARMSTADT, GERMANYE-mail: [email protected]

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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Articles
Copyright
© The Association for Symbolic Logic 2020

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