论文标题
Ackermann和Goodstein Go函数
Ackermann and Goodstein go functorial
论文作者
论文摘要
我们介绍了Goodstein定理的变体，这些变体等效于算术理解和算术递送递归，分别在弱基理论上。这些变体与通常的Goodstein定理不同，因为它们（必然）需要复杂的无限物体。作为证据的一部分，我们表明，序数上正常函数的Veblen层次结构与直接限制的Ackermann函数的扩展密切相关。
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.
