  The axiom Δ̰11-determinacy (equivalently, Borel-determinacy) is a theorem of ZFC and lies at the heart of the structure theory of Borel sets (and, in fact, the Σ̰11-sets and Σ̰12 sets). One virtue of ADL(ℝ) is that it lifts this entire structure theory from the Borel sets to the sets in L(ℝ). Summarizing results from above we have: 