$G_{\delta }$ semifilters and ${\omega }^{\ast }$

Will Brian, Jonathan Verner

The ultrafilters on the partial order $([\omega {]}^{\omega },{\subseteq }^{\ast })$ are the free ultrafilters on $\omega$, which constitute the space ${\omega }^{\ast }$, the Stone-Cech remainder of $\omega$. If $U$ is an uppers…