Dowker and super-Dowker filters

Abstract:

Our main results show that a very simple forcing construction can be used to add Dowker and super-Dowker filters:

Let $\kappa$ be uncountable with $\kappa ^{ < \kappa }=\kappa$. Let $G$ be generic over $V$ for $Add(\kappa , \kappa ^{++})$. Then in $V[G]$ there is a Dowker filter on $\kappa ^+$.

Let $V$ be Laver’s model in which $\kappa$ is supercompact and the supercompactness of $\kappa$ is indestructible under $\kappa$-directed closed forcing, and let $G$ be generic for $Add(\kappa , \kappa ^{++})$. Then in $V[G]$ there is a super-Dowker filter on $\kappa ^+$.