Preservation of splitting families and cardinal characteristics of the continuum

TL;DR

This paper develops a forcing technique to preserve splitting families during finite support iterations, enabling the construction of models with all 15 classical continuum characteristics pairwise distinct.

Contribution

It introduces a novel forcing method for preserving splitting families, allowing for the simultaneous separation of multiple continuum cardinal characteristics.

Findings

Constructed models with 15 continuum characteristics pairwise different.

Demonstrated preservation of splitting families under specific forcing iterations.

Separated key cardinal invariants in the continuum.

Abstract

We show how to construct, via forcing, splitting families than are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretely: the 10 (non-dependent) entries in Cicho\'n's diagram, $\mathfrak{m}(2\text{-Knaster})$, $\mathfrak{p}$, $\mathfrak{h}$, the splitting number $\mathfrak{s}$ and the reaping number $\mathfrak{r}$.