This will be a talk for the Notre Dame Logic Seminar on 6 February 2024, 2:00 pm.
![](https://jdh.hamkins.org/wp-content/uploads/Covering-reflection-1024x583.png)
Abstract. The principle of covering reflection holds of a cardinal $\kappa$ if for every structure $B$ in a countable first-order language there is a structure $A$ of size less than $\kappa$, such that $B$ is covered by elementary images of $A$ in $B$. Is there any such cardinal? Is the principle consistent? This is joint work with myself, Nai-Chung Hou, Andreas Lietz, and Farmer Schlutzenberg.