Splitting, Bounding, and Almost Disjointness can be quite Different

TL;DR

This paper demonstrates the consistency of a complex hierarchy of cardinal invariants in set theory, showing they can be independently assigned arbitrary uncountable regular values within ZFC.

Contribution

It establishes the consistency of a specific ordering and independence of several cardinal invariants related to measure and category in set theory.

Findings

Cardinal invariants can be assigned arbitrary uncountable regular values.

The paper proves the consistency of a detailed hierarchy of invariants.

It shows these invariants can be separated in ZFC.

Abstract

We prove the consistency of $\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{p}=\mathfrak{g}=\mathfrak{s}<\mathrm{add}(\mathcal{M})=\mathrm{cof}(\mathcal{M})<\mathfrak{a}=\mathrm{non}(\mathcal{N})=\mathfrak{c}$ with ZFC where each of these cardinal invariants assume arbitrary uncountable regular values.