The Pseudopower Dichotomy

Todd Eisworth

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arXiv · 2101.12687

The Pseudopower Dichotomy

Todd Eisworth

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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.

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BibTeX RIS

Todd Eisworth. 2022-12-15. The Pseudopower Dichotomy. https://arxiv.org/abs/2101.12687

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