Forcings constructed along morasses

Abstract

In a previous paper, we introduced a way of constructing a forcing along a simplified gap-1 morass such that the forcing satisfies a chain condition. Now, we generalize this to gap-2 morasses. As an application, we prove that GCH is consistent with the existence of a 0-dimensional Hausdorff topology on ${\omega }_3$ which has spread ${\omega }_1$.

accepted for the Journal of Symbolic Logic, various minor changes were made to the previous version