Dowker filters and Magidor forcing

Abstract: We prove that the consistency of the existence of a Dowker filter at $\kappa^+$ along with $2^{\kappa=\kappa+$} where $\kappa$ is regular and uncountable. Using Magidor forcing we also prove the consistency of the existence of a Dowker filter at $\mu^+$ where $\mu>{\rm cf}(\mu)>\omega$.