功能快速增长的层次结构
Functorial Fast-Growing Hierarchies
摘要：
快速增长的层次结构是通过各种类似的过程，产生乘法从加法，乘幂乘法等，我们观察到，快速增长的层次结构可以自然地扩展到函子的类别的自然数和线性顺序的函数序列。我们表明，二元快速增长的层次序数的范畴扩展是同构的序数崩溃功能所给出的指示系统，从而建立了证明论中的两个基本概念之间的连接。利用这一事实，我们得到了一个重述的子系统$Π^1_1$ -CA $_0$的分析作为一个更高的类型wellordering原则。
英文摘要：
Fast-growing hierarchies are sequences of functions obtained through various processes similar to the ones that yield multiplication from addition, exponentiation from multiplication, etc. We observe that fast-growing hierarchies can be naturally extended to functors on the categories of natural numbers and of linear orders. We show that the categorical extensions of binary fast-growing hierarchies to ordinals are isomorphic to denotation systems given by ordinal collapsing functions, thus establishing a connection between two fundamental concepts in Proof Theory. Using this fact, we obtain a restatement of the subsystem $Π^1_1$-CA$_0$ of analysis as a higher-type wellordering principle.
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