A series of lectures on Club_AD, February–March 2023

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 ${\mathrm{♣}}_{AD}$.

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 ${\mathrm{♣}}_{AD}$ and showed that PFA kills ${\mathrm{♣}}_{AD}$.

In the fourth lecture, we got ${\mathrm{♣}}_{AD}$ from a Souslin tree.

In the fifth lecture, we got ${\mathrm{♣}}_{AD}$ from a Luzin set.