ZFC的模型的上限序数的一个性质

A Property of Upper Bounded Ordinal of the Model of ZFC

中文摘要:

      

英文摘要:

      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.