正规函数的单不动点有多强？
How strong are single fixed points of normal functions?
摘要：
在M. Rathjen和本文作者证明了“每一个正规函数都有一个导数”的命题等价于$Π^1_1$ -条归纳法。在$\mathbf{ACA_0}$上证明了正规函数用扩张子表示的等价性。本文证明了“每个正规函数至少有一个不动点"等价于沿自然数的$Π^1_1$ -归纳法.
英文摘要：
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 $Π^1_1$-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 $Π^1_1$-induction along the natural numbers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
