| Résume | A structure $A$ covers a structure $B$ if every point of $B$ is contained in the range of an elementary embedding $j:A\rightarrow B$. The covering reflection property holds at a cardinal $\kappa$ if every structure in a countable language is covered by a structure of size less than $\kappa$. We discuss this property and show that the least cardinal with this property is a new type of large cardinal very high up in the large cardinal hierarchy. This is joint work with Hamkins, Hou and Schlutzenberg. |
