论文标题
中级古德斯坦原则
Intermediate Goodstein principles
论文作者
论文摘要
原始的Goodstein进程是通过在嵌套指数$ k $正常形式中编写自然数来进行的，然后将基础连续提高到$ k+1 $，然后从最终结果中减去一个。这样的序列始终达到零，但是在Peano算术中，这一事实是无法证实的。在本文中，我们根据Ackermann函数考虑自然数的符号。我们定义了三个新的GoodStein流程，获得了$ {\ sf aca} _0 $，$ {\ sf aca} _0' $和$ {\ sf aca} _0^+$的新独立结果，与存在与Turing的存在相关的二阶Arithmetic理论。
The original Goodstein process proceeds by writing natural numbers in nested exponential $k$-normal form, then successively raising the base to $k+1$ and subtracting one from the end result. Such sequences always reach zero, but this fact is unprovable in Peano arithmetic. In this paper we instead consider notations for natural numbers based on the Ackermann function. We define three new Goodstein processes, obtaining new independence results for $ {\sf ACA}_0$, ${\sf ACA}_0'$ and ${\sf ACA}_0^+$, theories of second order arithmetic related to the existence of Turing jumps.
