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 $\mu >\mathrm{cf}(\mu )>\omega$.