On the centeredness of saturated ideals

TL;DR

This paper investigates the properties of certain saturated ideals, demonstrating that Kunen's ideal over  is not centered and analyzing the saturation levels of Laver's ideal.

Contribution

It provides new insights into the centeredness and saturation properties of specific saturated ideals in set theory.

Findings

Kunen's saturated ideal over  is not centered

Laver's saturated ideal has limited saturation levels

Quantitative evaluation of saturation in terms of (,,<)

Abstract

We show that Kunen's saturated ideal over $\aleph_1$ is not centered. We also evaluate the extent of saturation of Laver's saturated ideal in terms of $(\kappa,\lambda,<\nu)$-saturation.