Chang's Conjecture, The Weak Reflection Principle and the Tree Property at $\omega_2$

TL;DR

This paper demonstrates that under certain strong set-theoretic assumptions, specifically a strong version of Chang's Conjecture and the Weak Reflection Principle at , there are no -Aronszajn trees, contributing to the understanding of tree properties at .

Contribution

It establishes a link between a strong form of Chang's Conjecture, the Weak Reflection Principle, and the non-existence of -Aronszajn trees.

Findings

Strong Chang's Conjecture implies no -Aronszajn trees.

Weak Reflection Principle at  is equivalent to a strong version of Chang's Conjecture.

Assuming continuum equals , no -Aronszajn trees exist under these assumptions.

Abstract

We prove that a strong version of Chang's Conjecture, equivalent to the Weak Reflection Principle at $\omega_2$, together with $2^\omega=\omega_2$, imply there are no $\omega_2$-Aronszajn trees.