迭代递归Mahlo运算
Iterating the recursively Mahlo operations
摘要：
在本文中，我们解决一个问题：多远，我们可以降低递归Mahlo操作在较高的反射宇宙？或者形式上说：在集合论中，对于反射率更高的宇宙，递归性更低的Mahlo运算可以迭代多少？事实证明，在$Π_N$ -反射宇宙中，最低的递归Mahlo运算可以沿着$Σ_1$ -高度为$N-3$的指数序的塔迭代，我们所能做的就是这样的迭代。也就是说，$Π_N$ -反射宇宙的集合论在证明理论上可简化为沿着这样一个塔的操作的迭代。
英文摘要：
In this paper we address a problem: How far can we iterate lower recursively Mahlo operations in higher reflecting universes? Or formally: How much can lower recursively Mahlo operations be iterated in set theories for higher reflecting universes? It turns out that in $Π_N$-reflecting universes the lowest recursively Mahlo operation can be iterated along towers of $Σ_1$-exponential orderings of height $N-3$, and that all we can do is such iterations. Namely the set theory for $Π_N$-reflecting universes is proof-theoretically reducible to iterations of the operation along such a tower.
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