The 25th Takagi Lectures
13:35--14:35, October 18 (Sat), 2025
10:00--11:00, October 19 (Sun), 2025
NISSAY Lecture Hall
Graduate School of Mathematical Sciences
The University of Tokyo, Tokyo, Japan


Lecture 1: The AD$^+$ Duality Program
Lecture 2: The HOD Conjecture and the Ultimate-$L$ Conjecture
W. Hugh Woodin
(Harvard University)


Abstract

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 sets of reals in a natural 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 sets of reals A for which AD$^+$ holds, and generalizations of $L$, the inner model of the universe of sets constructed by Gödel.