Chang's Conjecture, The Weak Reflection Principle and the Tree Property at $\omega_2$
Logic
2017-08-10 v2
Abstract
We prove that a strong version of Chang's Conjecture, equivalent to the Weak Reflection Principle at , together with , imply there are no -Aronszajn trees.
Keywords
Cite
@article{arxiv.1307.3731,
title = {Chang's Conjecture, The Weak Reflection Principle and the Tree Property at $\omega_2$},
author = {Victor Torres-Perez and Liuzhen Wu},
journal= {arXiv preprint arXiv:1307.3731},
year = {2017}
}
Comments
We prove indeed that $\mathrm{CC}^*+\lnot\mathrm{CH}$ imply the Tree Property for $\omega_2$ holds ($\mathrm{TP}(\omega_2)$). However, there was an error in our claim. It is not true that $\mathrm{CC}^*$ is equivalent to the Weak Reflection Principle at $\omega_2$ ($\mathrm{WRP}(\omega_2)$). The question if $\mathrm{WRP}(\omega_2)+\lnot\mathrm{CH}\rightarrow \mathrm{TP}(\omega_2)$ remains open