As part of the Thematic Program on Set Theoretic Methods in Algebra, Dynamics and Geometry (Fields Institute, January–June, 2023), Spencer Unger and I delivered a Graduate Course on Set Theory, Algebra and Analysis. My part of the course was a series of lectures around the guessing principle $\clubsuit_{AD}$.
The first lecture motivated the Dowker space problem and dealt with the Ostaszewski’s club principle.
The second lecture discussed the diamond and stick principles.
In the third lecture, we constructed a Dowker space from $\clubsuit_{AD}$ and showed that PFA kills $\clubsuit_{AD}$.
In the fourth lecture, we got $\clubsuit_{AD}$ from a Souslin tree.
In the fifth lecture, we got $\clubsuit_{AD}$ from a Luzin set.
