Towards stratification of Sealing Theorems

Sealing Theorems are very strong generic absoluteness principles formulated by Hugh Woodin. Whether the strongest one of them follows from the existence of some large cardinal is an open problem, very important in inner model theory.
We will survey how presence of large cardinals implies various generic absolutenesses, give some remarks on Sealing Theorems and outline ongoing project, which focuses on proving weak forms of Sealing from large cardinal axioms and finding their consistency strength. The project is joint with Grigor Sargsyan.