Superclub, splitting, separating statements

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.

Extended introduction, references

References in corpus (4)

• Negating the Galvin Property
• Tiltan and superclub
• Tiltan and graphs with no infinite paths
• Hungarian Cubes