The Cardinal Function pp(λ)

Abstract

In this chapter, we introduce Shelah’s cardinal function pp k (λ) whose properties we now summarize. If λ is a singular cardinal, then the definition of pp k (λ) gives pp k (λ) ≤ λ k for any cardinal k with cf (λ) ≤ k < λ. For singular cardinals λ with uncountable cofinality and k = cf (λ) which are in addition k-strong, we get pp k (λ) = λ k . In particular pp k (λ) = 2λ holds for every strong limit cardinal λ with uncountable cofinality k.