The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps

Abstract

Assuming the existence of a strong cardinal $\kappa$, a weakly compact cardinal $\lambda$ above it and $\gamma >\lambda ,$ we force a generic extension in which $\kappa$ is a singular strong limit cardinal of any given cofinality $\delta$, $2^{\kappa }\ge \gamma$ and such that the tree property holds at ${\kappa }^{++}$.