English

The Galvin property at $\kappa^{++}$ and not at $\kappa^+$

Logic 2025-08-21 v1

Abstract

We construct a κ\kappa-complete ultrafilter WW over κ\kappa such that ¬\negGal(κ,W,κ+)(\kappa, W, \kappa^+) and Gal(κ,W,κ++)(\kappa, W, \kappa^{++}). This answers a question of T. Benhamou and G. Goldberg.

Keywords

Cite

@article{arxiv.2508.14619,
  title  = {The Galvin property at $\kappa^{++}$ and not at $\kappa^+$},
  author = {Moti Gitik and Shachar Herpe},
  journal= {arXiv preprint arXiv:2508.14619},
  year   = {2025}
}