We will discuss various compactness principles such as stationary reflection, the tree property or Rado conjecture at small cardinals (for instance \(\omega_2\)). We will give context and motivation for the principles and discuss and compare the main sources of these principles: large cardinals and consequences of forcing axioms. We will focus on indestructibility of these principles with respect to classes of forcing notions, and give some examples (for instance we show that stationary reflection at \(\omega_2\) cannot be destroyed by a ccc forcing). Indestructibility is important for investigating connections between compactness and other areas of set theory such as generalized cardinal invariants, and we will mention some applications.

This talk will be given in mixed mode, in person as well as via Zoom.

If you want to attend in person, please be aware of the fact that you will be required to show proof of your COVID-19 "2.5G" status (vaccinated, recovered, PCR tested) upon entry of the buildings, or during sporadic random checks in the seminar rooms. During the lectures we will also pass around an attendance sheet to facilitate contact tracing. (According to the regulations, this form will be kept for 28 days and destroyed thereafter.)