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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 \lt n \lt \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.