## Past Seminars- Logic Set Theory

• Trevor Wilson
Mon Jan 14, 2013
4:00 pm
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...
• Nam Trang
Mon Jan 7, 2013
4:00 pm
We define a hierarchy of normal fine measures \mu_\alpha on some set X_\alpha and discuss the consistency strength of the theory (T_\alpha) =AD^+ + there is a normal fine measure \mu_\alpha on X_\alpha." These measures arise naturally from AD_R, which implies the determinacy of real games of fixed countable length. We discuss the construction of...
• Geoff Galgon
Mon Dec 3, 2012
4:00 pm
We continue with basic information on proper forcing.
• Sean Cox
Mon Nov 26, 2012
4:00 pm
Laver functions for supercompact cardinals appear in many forcing constructions, including all known constructions of models of strong forcing axioms. Viale proved that the Proper Forcing Axiom implies the existence of a "generic" Laver function from $\omega_2 \to H_{\omega_2}$. I will discuss his result and some recent work of mine on generic...
• Geoff Galgon
Mon Nov 19, 2012
4:00 pm
Basic facts about proper forcing will be presented.
• Martin Zeman
Mon Oct 29, 2012
4:00 pm
We finish the presentation of Laver preparation from the last week.
• Ryan Holben
Mon Oct 22, 2012
4:00 pm
The classical Theorem of Laver on making a supercompact cardinal indestructible will be presented.