论文标题
功能性快速增长的层次结构
Functorial Fast-Growing Hierarchies
论文作者
论文摘要
快速增长的层次结构是通过各种过程获得的函数序列，类似于从添加，乘法等产生乘法的过程。我们观察到，快速增长的层次结构可以自然地扩展到自然数和线性顺序类别的函子。我们表明，二进制快速增长的层次结构与序数的分类扩展是由序数崩溃函数给出的指示系统的同构，从而在证明理论中建立了两个基本概念之间的联系。 使用这个事实，我们获得了子系统$π^1_1 $ -CA $ _0分析的重述，作为高级井井有序的原理。
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.
