The Apter-Gitik birthday conference, May 2015

I give an invited (blackboard) talk at the Apter-Gitik birthday conference, Carnegie Mellon University, May 30-31 2015.

 Title: Putting a diamond inside the square.

Abstract: By a 35-year-old theorem of Shelah, ${\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}}_{\lambda }+\mathrm{♢}({\lambda }^{+})$ does not imply square-with-built-in-diamond_lambda for regular uncountable cardinals $\lambda$.

In this talk, I will sketch the proof from my recent paper, stating that ${\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◻"\; src="https://s.w.org/images/core/emoji/15.0.3/svg/25fb.svg">}}_{\lambda }+\mathrm{♢}({\lambda }^{+})$ is equivalent to square-with-built-in-diamond_lambda for every singular cardinal $\lambda$.