Cicho\'n's Diagram and Localisation Cardinals

TL;DR

This paper reimplements a creature forcing method to separate Cichoń's diagram into five cardinals and extends it by adding numerous localisation cardinals, enriching the understanding of cardinal characteristics.

Contribution

It introduces a countable support product construction that separates Cichoń's diagram and incorporates uncountably many localisation cardinals, advancing the study of cardinal characteristics.

Findings

Separated Cichoń's diagram into five cardinals

Extended the construction with uncountably many localisation cardinals

Demonstrated the countable support product's effectiveness

Abstract

We reimplement the creature forcing construction used by Fischer et al. (arXiv:1402.0367) to separate Cicho\'{n}'s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.