3 problems

Let $\nu$ be a singular limit of supercompact cardinals, and let $\nu^+$ denote its successor cardinal. The super tree property conjecture. The cardinal $\nu^+$ satisfies the super…

Let $\langle \kappa_n\rangle_{n<\omega}$ be an infinite sequence of supercompact cardinals, and let $\mathbb{R}_{\omega}$ be the Cummings–Foreman forcing iteration that produces a…

Let $\mathbb{R}_{\omega}$ be the forcing defined by Cummings and Foreman from an infinite sequence of supercompact cardinals, producing a model in which every $\aleph_n$ for…