Chang 猜想、弱反射原理与 $\omega_2$ 处的树性质
逻辑
2017-08-10 v2
摘要
我们证明了 Chang 猜想的一个强版本（等价于 处的弱反射原理）连同 ，蕴含不存在 -Aronszajn 树。
引用
@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}
}
备注
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