
THEMATIC PROGRAMS 

September 30, 2023  
Set Theory and Analysis ProgramCoxeter Lecture Series Hugh Woodin, University of California, Berkeley 1) The Continuum Hypothesis and the $\Omega$ Conjecture 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 
