# Trevor Wilson: Semi-scales on $\Pi^2_1$ sets

Monday, January 14, 2013, at 4pm
RH 440R

Speaker: Trevor Wilson (UCI)

Title: Semi-scales on $\Pi^2_1$ sets

Abstract:

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.