SCH and stronger tree proeprties
Abstract: Stronger tree properties capture the combinatorial essence of large cardinals. For an inaccessible cardinals $\kappa$, $\kappa$ is strongly (resp. super) compact if and only of $\kappa$ has the strong (resp. super) tree property. A famous theorem of Solovay is that SCH holds above a strongly compact cardinal. This leads to the question of whether the strong or super tree property imply SCH above. One strategy for a positive answer is to use internally unbounded models. We will show the consistency of the super tree property (ITP) holds at the double successor of a singular together with club many non-internally unbounded models, which points to a negative answer. Our construction uses extender based forcing. This is joint work with Sherwood Hachtman.
Tuesday February 6, 2018 at 3:30 PM in SEO 427