## Logic Seminar

Martin Zeman

University of California Irvine

Constructing iteration strategies for background certified extender models in the presence of Woodin cardinals

**Abstract:**It is a well-known fact that that if a background certified extender model has a Woodin cardinal then it may not have an iteration strategy. The question whether such an iteration strategy exists turns out to depend on the universe in which such a model is constructed. We give an example of such a universe (another example was obtained by Woodin some time ago), and describe an iteration strategy for the background certified model K^c constructed in this universe. In this situation the model K^c may contain many Woodin cardinals, but needs to be tame. Generalizations for the non-tame case are being considered, but have not been fully worked out. This is a joint work with Grigor Sargsyan.

Tuesday April 10, 2018 at 3:30 PM in SEO 427