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arXiv · 1906.09307

Representability and Compactness for Pseudopowers

Todd Eisworth
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Abstract

We prove a compactness theorem for pseudopower operations of the form $pp_{Γ(μ,σ)}(μ)$ where $\aleph_0<σ=cf(σ)\leq cf(μ)$. Our main tool is a result that has Shelah's cov vs. 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 $pcf(A)$ has an inaccessible accumulation point.

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Todd Eisworth. 2019-06-21. Representability and Compactness for Pseudopowers. https://arxiv.org/abs/1906.09307

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