The goal of the Foreman-Magidor program was to show that large cardinal axioms also implied that the third version of CH held for all sets in L(ℝ) and, more generally, all universally Baire sets. In other words, the goal was to show that large cardinal axioms implied that ΘL(ℝ) ≤ ℵ2 and, more generally, that ΘL(A,ℝ) ≤ ℵ2 for each universally Baire set A. 