The AD+ Duality Program

The study of descriptive set theory in the context of determinacy axioms began nearly 60 years ago. The context for this study is now understood to be the Axiom AD+, which is a refinement of the Axiom of Determinacy (AD).  The objects of this study are the universally Baire sets of reals which form a transfinite  hierarchy which extends the borel sets.

This has led to what is arguably the main duality program of Set Theory, which is the connection between the universally Baire sets,  and generalizations of L, the inner model of the universe of sets constructed by Gödel.