Speaker: 

Trevor Wilson

Institution: 

UCI

Time: 

Monday, January 14, 2013 - 4:00pm to 5:30pm

Host: 

We prove a theorem of Woodin that, assuming $\mathsf{ZF} + \mathsf{AD}+ \theta_0 < \Theta$, every $\Pi^2_1$ set of reals has a semi-scale whose norms are ordinal-definable.  The consequence of $\mathsf{AD}+\theta_0 < \Theta$ that we use is the existence of a countably complete fine measure on a certain set, which itself is a set of measures.  If time permits, we outline how "semi-scale" can be improved to "scale" in the theorem using a technique of Jackson.