Pseudo P-points and splitting number

TL;DR

This paper constructs a model demonstrating that the splitting number can be large while all ultrafilters lack pseudo-intersections for small subsets, highlighting a novel interaction between these set-theoretic concepts.

Contribution

It introduces a new model where the splitting number is large and ultrafilters have small subsets without pseudo-intersections, revealing novel set-theoretic relationships.

Findings

Large splitting number in the constructed model

Ultrafilters lack pseudo-intersections for small subsets

New interaction between splitting number and ultrafilter properties

Abstract

We construct a model in which the splitting number is large and every ultrafilter has a small subset with no pseudo-intersection.