We prove a compactness theorem for pseudopower operations of the form \({{\,\mathrm{pp}\,}}_{\Gamma (\mu ,\sigma )}(\mu )\) where \(\aleph _0<\sigma ={{\,\mathrm{cf}\,}}(\sigma )\le {{\,\mathrm{cf}\,}}(\mu )\). Our main tool is a result that has Shelah’s cov versus pp Theorem as a consequence. We also show that the failure of compactness in other situations has significant consequences for pcf theory, in particular, implying the existence of a progressive set A of regular cardinals for which \({{\,\mathrm{pcf}\,}}(A)\) has an inaccessible accumulation point.

我们证明了\({{\,\mathrm{pp}\,}}_{\Gamma (\mu ,\sigma )}(\mu )\)形式的伪幂运算的紧致定理，其中\(\aleph _0 <\sigma ={{\,\mathrm{cf}\,}}(\sigma )\le {{\,\mathrm{cf}\,}}(\mu )\)。我们的主要工具是一个结果，其结果是 Shelah 的 cov 与 pp 定理。我们还表明，在其他情况下紧致性的失败对 pcf 理论有重大影响，特别是，这意味着存在正则基数的渐进集合A，其中\({{\,\mathrm{pcf}\,}}( A)\)有一个无法到达的聚集点。