Nam Trang


University of North Texas, Denton


Monday, May 20, 2019 - 4:00pm to 5:30pm




Sealing is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by forcing. generic-LSA is the statement that the Largest Suslin Axiom (LSA) holds in all generic extensions. Under a mild large cardinal hypothesis, we show that Sealing is equiconsistent with generic-LSA. As a consequence, Sealing is weaker than the theory ``ZFC+there is a Woodin cardinal which is a limit of Woodin cardinals". Sealing's consistency being weak represents an obstruction to the current program of descriptive inner model theory. Going beyond this bound in core model induction applications seems challenging and requires us to construct third order objects (subsets of the universally Baire sets). We will state the precise theorems and discuss their impact on current developments of inner model theory. Time allowed, we will talk a bit about how to overcome the the obstructions imposed by Sealing. This is joint work with G. Sargsyan.