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 $$\cov(\mu,\mu,\theta,\sigma)=\cov(\mu,\mu,(\cf\mu)^+,\sigma)+\cov(\mu,\mu,\theta,\sigma^+)$$ whenever $\aleph_1\leq\sigma=\cf(\sigma)<\cf(\mu)<\theta<\mu$, and use recent work of Gitik to show that both summands in the equation are required.