|Time:|| 12:00 - 13:20
Baker Hall 150
Department of Mathematical Sciences
Inner model theory (series of three talks)
Jensen proved that the combinatorial principle "square" holds in L. I will outline the proof of this theorem, as well as that of Jensen's "covering lemma" for L, which also involves "fine structure". This will lead into a discussion of large cardinals and mice. I expect this will take two lectures. Ultimately, inner model theory combines fine structure and iteration trees, but that is beyond the scope of these lectures. Instead, the third lecture will be on forcing with Woodin's extender algebra because the proofs are reminiscent of how iteration trees are used in inner model theory, and because the extender algebra is used in applications of inner model theory to descriptive set theory.