The Pseudopower Dichotomy

Abstract

We investigate pseudopowers of singular cardinals, and show that deduce some consequences for cardinal arithmetic. For example, we show that in {\sf ZFC} that $$\cov(μ,μ,θ,σ)=\cov(μ,μ,(\cfμ)^+,σ)+\cov(μ,μ,θ,σ^+)$$ whenever $\aleph_1\leqσ=\cf(σ)<\cf(μ)<θ<μ$, and use recent work of Gitik to show that both summands in the equation are required.

26 pages. Minor revisions to previous version. Submitted to Journal of Symbolic Logic