Tree properties are a family of combinatorial principles that characterize large cardinal properties for inaccessibles, but can consistently hold for "small" (successor) cardinals such as $\aleph_2$.  It is a classic theorem of Magidor and Shelah that if $\kappa$ is the singular limit of supercompact cardinals, then $\kappa^+$ has the tree property.  Neeman showed how to force $\kappa^+$ to become $\aleph_{\omega+1}$ while maintaining the tree property.  Fontanella generalized these results to the strong tree property.

We show (in ZFC) that if $\kappa$ is a singular limit of supercompact cardinals, then $\kappa^+$ has the super tree property (this jump from "strong" to "super" is analogous to the jump in strength from strongly to supercompact cardinals).  We remark on how to get the super tree property at $\aleph_{\omega+1}$, and on some interesting consequences for the existence of guessing models at successors of singulars.  This is joint work with Dima Sinapova.