中科院数学与系统科学研究院
数学研究所
集合论研讨班报告
报告人： 申国桢 博士（中科院数学院）
题 目：Powers and factorials of non-well-ordered cardinals
时 间：2019.12.19（星期四）, 13:00-15:00
地 点：数学院南楼N902室
摘 要：In this talk, we summarize known results concerning powers and factorials of non-well-ordered cardinals. Among these results, we shall prove Halbeisen and Shelah's theorem which states that $2^\mathfrak{a}\neq\mathrm{seq}^{1\text{-}1}(\mathfrak{a})$ for all infinite cardinals $\mathfrak{a}$. We also prove that the existence of an infinite set $x$ such that there is a finite-to-one function from $x!$ onto $x$ is consistent with ZF.
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