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HOW STRONG ARE SINGLE FIXED POINTS OF NORMAL FUNCTIONS?
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 85 / Issue 2 / June 2020
- Published online by Cambridge University Press:
- 20 July 2020, pp. 709-732
- Print publication:
- June 2020
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- Article
- Export citation
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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.
