Forcings constructed along morasses

TL;DR

This paper generalizes a method for constructing forcings along morasses, extending previous work from gap-1 to gap-2, and applies it to show the consistency of certain topological and set-theoretic properties.

Contribution

It introduces a generalized forcing construction along gap-2 morasses and demonstrates its application to set theory and topology.

Findings

Established a forcing construction along gap-2 morasses

Proved GCH is consistent with a specific topology on ω₃

Extended previous methods from gap-1 to gap-2 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 $\omega_1$.