March 1
Chris Lambie-Hanson,
Virginia Commonwealth University
The C-sequence number
The C-sequence number of an uncountable regular cardinal $\kappa$ is a cardinal invariant that provides a measure of the amount of compactness that holds at $\kappa$. We will begin this talk by introducing the C-sequence number and proving some of its basic properties, linking it to familiar notions including large cardinals and square principles. We will then outline a number of consistency results regarding the C-sequence number at inaccessible cardinals and successors of singular cardinals. We will end by exploring how the C-sequence number interacts with the existence of complicated colorings and the infinite productivity of the $\kappa$-Knaster condition. This is joint work with Assaf Rinot.