Academics

Large cardinals and small sets: The AD+ Duality Program

Time: Wednesday, November 9, 2022 22:30-24:00 Beijing time

Venue:online

Speaker:Hugh Woodin

Speaker: Hugh Woodin

W. Hugh Woodin is a Distinguished Professor Emeritus of Mathematics at the University of California, Berkeley and a Professor of Philosophy and of Mathematics at Harvard University. Woodin is a leading set theorist. He has made many notable contributions to the theory of inner models and determinacy, to functional analysis, and recursion theory. A type of large cardinal, the Woodin cardinal, bears his name. He is a managing editor of the Journal of Mathematical Logic. In 1989 he received the Carol Karp Prize from the Association for Symbolic Logic.


Abstract

The determinacy axiom, AD, was introduced by Mycielski and Steinhaus over 60 years ago as an alternative to the Axiom of Choice for the study of arbitrary sets of real numbers. The modern view is that determinacy axioms concern generalizations of the borel sets, and deep connections with large cardinal axioms have emerged.

The study of determinacy axioms has led to a specific technical refinement of AD, this is the axiom AD+. The further connections with large axioms have in turn implicitly led to a duality program, this is the AD+ Duality Program.

The main open problems here are intertwined with those of the Inner Model Program, which is the central program in the study of large cardinal axioms.

This has now all been distilled into a series of specific conjectures.

A61FB


DATENovember 9, 2022
SHARE
Related News
    • 0

      Scaling Law-based Functional Clustering: A Statistical Model for Compressing Large Multimodal Models

      AbstractModels across different application domains are exploding in size. This disproportionate increase in model sizes will quickly obstruct the sustainability of deep learning. From my personal view, functional clustering, a model derived to classify a population of variables into distinct modules, can serve as an alternative tool to compress and optimize large multimodal models in any size....

    • 1

      Sharp Moser-Trudinger inequalities and nonlocal Moser-Trudinger equation

      摘要:This is an summary talk for Moser-Trudinger inequality. In this talk, I first introduce the classical Moser-Trudinger inequalities in bounded domain and unbounded domain. Then I will present the work on the existence and no-existence for extremals of Moser-Trudinger inequality. The Trace-type Moser-Trudinger inequality in bounded and unbounded domain will be also discussed in this talk. F...