# Cicho\'n's maximum without large cardinals

## TL;DR

This paper proves the consistency of all twelve cardinal characteristics in Cichoń's diagram being pairwise different without relying on large cardinal assumptions, which was previously unachievable.

## Contribution

It demonstrates the consistency of Cichoń's diagram with all entries pairwise distinct without large cardinal hypotheses, advancing understanding in set theory.

## Key findings

- All entries of Cichoń's diagram can be pairwise different without large cardinals.
- Established new consistency results in set theory.
- Removed the need for large cardinal assumptions in this context.

## Abstract

Cicho\'n's diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets of the irrationals. It is consistent that all entries of Cicho\'n's diagram are pairwise different (apart from $\textrm{add}(\mathcal{M})$ and $\textrm{cof}(\mathcal{M})$, which are provably equal to other entries). However, the consistency proofs so far required large cardinal assumptions. In this work, we show the consistency without such assumptions.