September 30, 2023

Set Theory and Analysis Program

Coxeter Lecture Series

Hugh Woodin, University of California, Berkeley
November 4, 5, 6, 3:30 - 5:00

Audio of talks

1) The Continuum Hypothesis and the $\Omega$ Conjecture
2) Strong Axioms: Determinacy and Large Cardinals
3) Extender Sequences and Beyond

One compelling approach to resolving the Continuum Hypothesis is to look for "generically absolute" theories for $H(\omega_2)$ which informally can be thought of as the structure of all subsets of the least uncountable cardinal, $\omega_1$, or alternatively as the structure of all $\omega_1$ sequences of reals numbers.

If the $\Omega$ Conjecture is true the criterion of generic absoluteness is equivalent to validity in $\Omega$ logic. In this case there {\em are} such good theories for $H(\omega_2)$ but any such theory necessarily implies that the Continuum Hypothesis is false.

This analysis draws on the considerable machinery which has been developed over the last several decades for analyzing inner models in which the Axiom of Determinacy holds. An important component has been the adapting of techniques from the study of inner models of large cardinals to the study of inner models of determinacy.

An overview of some of the key ideas will be given.

For more details on the thematic year, see Program Page