论文标题
巨人和幻觉巨型古斯坦原理
Giant and illusionary giant Goodstein principles
论文作者
论文摘要
我们分析了几种自然的古德斯坦原理，这些原则本身是针对Ackermann函数和扩展的Ackermann函数定义的。这些Ackermann功能是完善的规范快速增长功能，该功能由不超过$ \ varepsilon_0 $的序数标记。在正在考虑的Goodsteinprinciples中，巨型巨人将在理论上是强大的（在Ackermannian案件中无法证明$ \ Mathrm {pa} $，并且在$ \ Mathrm {id} _1中无法证明是在较大的Ackermann案例中的差异很大的一面，但在其他方面，他们的景点很薄弱，与众不同的是，他们的景点很弱。
We analyze several natural Goodstein principles which themselves are defined with respect to the Ackermann function and the extended Ackermann function. These Ackermann functions are well established canonical fast growing functions labeled by ordinals not exceeding $\varepsilon_0$. Among the Goodsteinprinciples under consideration, the giant ones, will be proof-theoretically strong (being unprovable in $\mathrm{PA}$ in the Ackermannian case and being unprovable in $\mathrm{ID}_1$ in the extended Ackermannian case) whereas others, the illusionary giant ones, will turn out to be comparatively much much weaker although they look strong at first sight.
