Tree Properties at Successors of Singulars of Many Cofinalities

Abstract: From many supercompact cardinals, we show that it is consistent for the tree property to hold at many small successors of singular cardinals, each with a different cofinality. In particular, we construct a model in which the tree property holds at $\aleph_{\omega+\omega+1}$ and at $\aleph_{\omega_n+1}$ for all $0<n<\omega$. We show that this can be done for the strong tree property as well, and extend the technique to large uncountable sequences of desired cofinalities.