The left side of Cicho\'n's diagram

TL;DR

This paper constructs a model demonstrating a specific strict inequality chain among cardinal characteristics of the continuum using finite support iteration of ccc forcings.

Contribution

It introduces a novel forcing construction that achieves a particular configuration of cardinal invariants within Cichoń's diagram.

Findings

Established a model with the specified inequalities among cardinal characteristics.

Demonstrated the consistency of this configuration using ccc forcing techniques.

Contributed to the understanding of possible arrangements of invariants in set theory.

Abstract

Using a finite support iteration of ccc forcings, we construct a model of $\aleph_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})=\mathfrak{c}$.