Superclub, splitting, separating statements

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2025年2月18日

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Shimon Garti,
Saharon Shelah

摘要

We prove that superclub implies $\mathfrak {s}=\omega _1$ $s = ω_{1}$ . More generally, if $\kappa $ $κ$ is weakly compact then superclub implies $\mathfrak {s}_\kappa =\kappa ^+$ $s_{κ} = κ^{+}$ . Based on this statement, we separate tiltan from superclub at successors of supercompact cardinals. We also use the Galvin property in order to separate tiltan from superclub at both successors of regular and successors of singular cardinals.