# Assaf Rinot: Putting a diamond inside the square

Infinite Combinatorics Seminar (BIU)

25/January/2015, 10:15-12:00,
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.