# Split Principles

## TL;DR

This paper introduces split principles, revealing their deep connections to large cardinal properties and classical combinatorial objects, and establishing correspondences with splitting numbers at uncountable cardinals.

## Contribution

It presents the split principles and explores their relationships with large cardinals, combinatorial objects, and splitting numbers, providing new insights into set theory.

## Key findings

- Split principles are tightly connected to large cardinal properties.
- Correspondences between split principles and splitting numbers are established.
- The paper links split principles to classical combinatorial objects like Aronszajn and Souslin trees.

## Abstract

We introduce the split principles and show that they bear tight connections to large cardinal properties such as inaccessibility, weak compactness, subtlety, almost ineffability and ineffability, as well as classical combinatorial objects such as Aronszajn trees, Souslin trees or square principles. We exhibit correspondences between certain split principles and splitting numbers at uncountable cardinals.