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申国桢 博士： Powers and factorials of non-well-ordered cardinals

本站小编 Free考研/2020-05-19


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 申国桢 博士，中科院数学院
Inviter:
Title:
 Powers and factorials of non-well-ordered cardinals
Time & Venue:
 2019.12.19 13:00-15:00 N902
Abstract:
 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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