The Katowice problem and autohomeomorphisms of ${\omega }^{\ast }$

David Chodounsky, Alan Dow, Klaas Pieter Hart +1

We show that the existence of a homeomorphism between ${\omega }_0^{\ast }$ and ${\omega }_1^{\ast }$ entails the existence of a non-trivial autohomeomorphism of ${\omega }_0^{\ast }$.