Towers in \([\omega]^{\omega}\) and \(^{\omega}\omega\)
The author studies the sets \(A=\{\kappa |\) there is a \(\kappa\)-tower in \([\omega]^{\omega}\}\) and \(B=\{\kappa |\) there is a \(\kappa\)- tower in \(^{\omega}\omega \}\), and shows that in ZFC either \(B\subseteq A\) or else there is a scale in \(^{\omega}\omega\). The bulk of the paper consists of forcing extensions in which A (and possibly B, too) can be certain preassigned sets and various relationships hold between cardinals associated with the respective partial orderings.
cardinals associated with partial orderings
scientific article; zbMATH DE number 4123716
scientific article