ZFC的模型的上限序数的一个性质

S1 引言 Forcing方法假设存在ZFC的一个可数可传的模型M。记满足αM的最小序数α为,显然M中一切序数所成的集合即。由于M是ZFC的模型,故应具有某些性质。本文证明了它满足关系,故为ε数或1级关键数,进而证明了是H级关键数(H为任意自然数)。文中的记号等引用。

A Property of Upper Bounded Ordinal of the Model of ZFC

Forcing has assumed that there is a countable transitive model of ZFC. The least ordinal which is not in the model is called it's upper bounded ordinal. In this paper the critical number of ordinal addition is called the zero-order's critical number, the fixed point of the enumerating function of the zero-order's critical number is called one-order's critical number, and so on. It is proved that the upper bounded ordinal is a k-order's critical number (k is an arbitrary natural number). Therefore, it is a huge ordinal in all countable ordinals.