I shall speak at the Rutgers Logic Seminar on April 21, 2014, 5:00-6:20 pm, Room 705, Hill Center, Busch Campus, Rutgers University.
Abstract. I will show that large cardinals, such as measurable, strong and supercompact cardinals, need not exhibit their large cardinal nature in HOD. Specifically, it is relatively consistent that a supercompact cardinal is not weakly compact in HOD, and one may construct models with a proper class of supercompact cardinals, none of them weakly compact in HOD. This is current joint work with Cheng Yong.