阿克曼和古德斯坦去函子
Ackermann and Goodstein go functorial
摘要：
我们提出的变种古德斯坦定理，相当于算术理解和算术超限递归，分别在弱基理论。这些变体不同于通常的古德斯坦定理，因为它们（必然）需要复杂的无限对象的存在。作为我们的证明的一部分，我们表明，凡勃伦层次的正规函数的序数是密切相关的扩展的阿克曼函数的直接限制。
英文摘要：
We present variants of Goodstein's theorem that are equivalent to arithmetical comprehension and to arithmetical transfinite recursion, respectively, over a weak base theory. These variants differ from the usual Goodstein theorem in that they (necessarily) entail the existence of complex infinite objects. As part of our proof, we show that the Veblen hierarchy of normal functions on the ordinals is closely related to an extension of the Ackermann function by direct limits.
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