论文标题
Bachmann-Howard Oldinal的基本序列和快速增长的层次结构
Fundamental sequences and fast-growing hierarchies for the Bachmann-Howard ordinal
论文作者
论文摘要
我们证明，$ \ vartheta $函数的布赫霍尔兹（Buchholz）的基本序列系统享有各种规律性条件，包括Bachmann属性。我们将这些结果部分扩展到$ \ vartheta $函数的变体，包括一个不添加可数序的版本。我们得出的结论是，基于这些符号系统的强壮函数享有自然单调性属性，并将沿$ \ vartheta（\ varepsilon_ {ω+1}）$沿原始递归定义的所有功能进行了主要化。
We prove that Buchholz's system of fundamental sequences for the $\vartheta$ function enjoys various regularity conditions, including the Bachmann property. We partially extend these results to variants of the $\vartheta$ function, including a version without addition for countable ordinals. We conclude that the Hardy functions based on these notation systems enjoy natural monotonicity properties and majorize all functions defined by primitive recursion along $\vartheta(\varepsilon_{Ω+1})$.
