The ABCs of PCF, with applications to Dowker spaces

In this two-part series, we will begin by surveying the basics of Shelah's theory of Possible Cofinalities (PCF), focusing in particular on a foundational theorem about the existence of scales. We will then transition into using PCF to construct a Dowker space whose cardinality is fixed within ZFC. The main idea will be to use such a "scale" to build  a particularly nice closed, unbounded subset of Rudin's original Dowker space. No prior knowledge of PCF will be assumed.