English

Superclub, splitting, separating statements

Logic 2025-05-28 v2

Abstract

We prove that superclub implies s=1\mathfrak{s}=\aleph_1. More generally, superclub at a successor of a weakly compact cardinal implies sκ=κ+\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.

Cite

@article{arxiv.2302.00904,
  title  = {Superclub, splitting, separating statements},
  author = {Shimon Garti and Saharon Shelah},
  journal= {arXiv preprint arXiv:2302.00904},
  year   = {2025}
}

Comments

Extended introduction, references

R2 v1 2026-06-28T08:29:56.096Z