Müller, S. (2022, July 6). Preserving universally Baire Sets and Sealing [Conference Presentation]. Set Theory Workshop am Erwin Schrödinger Institut, Wien, Austria.
Universally Baire sets play a central role in many areas of set theory. In inner model theory many objects we construct are universally Baire and this is crucial as it allows us to extend them onto generic extensions. Sealing, a generic absoluteness principle for the theory of the universally Baire sets introduced by Woodin, is therefore an obstruction to construct canonical inner models. In his famous Sealing Theorem, Woodin showed that in the presence of a proper class of Woodin cardinals Sealing holds after collapsing 22κ for a supercompact cardinal κ. We will outline a new and stationary-tower-free proof of Woodin’s Sealing Theorem that is based on Sargsyan’s and Trang’s proof of Sealing from iterability. A key new technical concept in our proof is the preservation of universally Baire sets in ultrapowers by extenders. This is joint work with Grigor Sargsyan and Bartosz Wcisło.
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Project title:
Lange Spiele und Determiniertheit wenn alle Mengen uB sind: V 844_N (Fonds zur Förderung der wissenschaftlichen Forschung (FWF))