Dowker filters and Magidor forcing

TL;DR

This paper establishes the consistency of Dowker filters at successor cardinals under certain set-theoretic assumptions, using advanced forcing techniques to extend known results.

Contribution

It proves the consistency of Dowker filters at successor cardinals with specific cardinal arithmetic, employing Magidor forcing to generalize previous results.

Findings

Consistency of Dowker filters at ^+ with 2^=^+ for regular .

Consistency of Dowker filters at ^+ where > ext{cf}()> ext{omega}.

Application of Magidor forcing to construct models with Dowker filters.

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