# Yair Hayut: Subcompact cardinals

TAU forcing seminar

On 04/Dec/17, 9-11, Yair Hayut will be speaking on Subcompact cardinals.

Abstract. During the investigation of the existence of squares in core models, Jensen isolated the concept of subcompact cardinals. Subcompactness is weaker than supercompactness and stronger than superstrength. It is a natural candidate for the consistency strength of simultaneous failure of $\square(\kappa)$ and $\square_\kappa$. A work of Schimmerling and Zeman indicates that under some mild assumptions, subcompactness is the only possibility for failure of squares at core models of the form L[E].

In this talk I will define the relevant large cardinals notions, and talk about Zeman’s theorem for the consistency of failure $\square_{\aleph_{\omega}}$ from a measurable subcompact cardinal.