论选择公理与2^(■_0)≥■_1的关系

On Relation between Axiom of Choice and 2^(■_0)≥■_1

那汤松(HamaHcoH)在他所著的《实变函数》认为,不需要选择公理就可以证明2■0≥■1.证明,若ZF+AD是和谐的,则没有选择公理,2■0≥■1不成立.从而说明那汤松所提示的证明是不严格的.

In the book ＂Real Analysis＂, HamaHcoH claimed that he can prove 2N0≥N1 without the axiom of choice. We prove that, if ZF＋AD is consistent, then 2N0≥N1 can not hold without the axiom of choice.