Destructibility of the tree property at $\aleph_{\omega+1}$
  We construct a model in which the tree property holds in $\aleph_{\omega + 1}$ and it is destructible under $\text{Col}(\omega, \omega_1)$. On the other hand we discuss some cases in which the tree property is indestructible under small or closed forcings. 
Yair Hayut and Menachem Magidor
math.LO