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arXiv · 2302.00904

Superclub, splitting, separating statements

Shimon Garti·Saharon Shelah
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Abstract

We prove that superclub implies $\mathfrak{s}=\aleph_1$. More generally, superclub at a successor of a weakly compact cardinal implies $\mathfrak{s}_\kappa=\kappa^+$. Based on this statement, we separate tiltan from superclub at a successor of a supercompact cardinal. We use Galvin's property in order to separate tiltan from superclub at successors of both regular and singular cardinals.

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Shimon Garti, Saharon Shelah. 2023-02-02. Superclub, splitting, separating statements. https://doi.org/10.1007/s10998-025-00628-2

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