Logic Seminar
Grigor Sargsyan
Rutgers University
An upper bound for uB-sealing
Abstract: Woodin showed that, assuming the existence of a supercompact cardinal and a class of Woodin cardinals, after collapsing a supercompact cardinal to be countable,
the theory of L(Gamma_{uB}) is sealed. Here, Gamma_{uB} is the collection of the universally Baire sets of reals. We say that the theory of L(Gamma_{uB}) is sealed if for any V-generic
g and a V[g]-generic h, there is an elementary embedding j: L(Gamma_uB)^{V[g]}-> L(Gamma_uB)^{V[g*h]}. It has been conjectured by the speaker that sealing has a weak large cardinal strength,
and its weakness is the reason why the core model induction becomes so much more complicated after passing the threshold given by sealing. In a very recent work, the speaker and Trang
showed that sealing is indeed weak, weaker than a Woodin cardinal that is itself a limit of Woodin cardinals. After stating the relevant theorems we will outline why exactly the core model induction becomes
rather difficult after this threshold.
Tuesday November 20, 2018 at 3:30 PM in 427 SEO