Fragility and indestructibility of the tree property

We prove various theorems about the preservation and destruction of the tree property at ω ₂. Working in a model of Mitchell 9] where the tree property holds at ω ₂, we prove that ω ₂ still has the tree property after ccc forcing of size ${\aleph_1}$ or adding an arbitrary number of Cohen reals. We show that there is a relatively mild forcing in this same model which destroys the tree property. Finally we prove from a supercompact cardinal that the tree property at ω ₂ can be indestructible under ω ₂-directed closed forcing.