Infinite Combinatorics Seminar (BIU)
Room 201, Building 216, Bar-Ilan University
Speaker: Assaf Rinot
Title: Putting a diamond inside the square
Abstract: Gray’s combinatorial principle SD_k is a strong combination of Jensen’s $\square_\kappa$ and $\diamondsuit(\kappa^+)$ principles. This principle proved itself very useful in constructing uncountable graphs of counter-intuitive nature.
By a 35 year old theorem of Shelah, $\square_\kappa+\diamondsuit(\kappa^+)$ does not imply SD_k for regular uncountable cardinals $\kappa$. In this talk, I will prove that they are equivalent whenever $\kappa$ is singular.