Destructibility of the tree property at $\aleph_{ω+1}$
Yair Hayut, Menachem Magidor · arXiv (Cornell University) · 2016
We construct a model in which the tree property holds in $\aleph_{ω+ 1}$ and it is destructible under $\text{Col}(ω, ω_1)$. On the other hand we discuss some cases in which the tree property is indestructible under small or closed forcings.