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arXiv · 2501.10294

On the number of cofinalities of cuts in ultraproducts of linear orders

Mohammad Golshani
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Abstract

Suppose $κ$ is a regular cardinal and $\bar a=\langle μ_i: i<κ\rangle$ is a non-decreasing sequence of regular cardinals. We study the set of possible cofinalities of cuts Pcut$(\bar a)=\{(λ_1, λ_2):$ for some ultrafilter $D$ on $κ$, $(λ_1, λ_2)$ is the cofinality of a cut of $\prod\limits_{i<κ} μ_i / D \}$.

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Mohammad Golshani. 2025-01-17. On the number of cofinalities of cuts in ultraproducts of linear orders. https://arxiv.org/abs/2501.10294

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