Liuzhen Wu (Chinese Academy of Sciences)

A surjection from square onto power

Cantor proves that for any set $A$, there is no surjection from $A$ into its power set $\mathcal{P}(A)$. In this talk, we describe a construction of a ZF model. In this model, there is a set $A$ and a surjection from its square set $A^2$ onto its power set $\mathcal{P}(A)$. This indicates Cantor's Theorem is in some sense optimal. This is joint work with Guozhen Shen and Yinhe Peng.