**February 19**

**Philipp Lücke**,
University of Bonn

**Magidor-style embedding characterizations of large cardinals**

Motivated by a classical theorem of Magidor, I will present results providing characterizations of important objects from the lower end of the large cardinal hierarchy through the existence of elementary embeddings between set-sized models that map their critical point to the large cardinal in question. Focusing on the characterization of *shrewd cardinals*, introduced by Rathjen in a proof-theoretic context, I will show how these results can be used in the study of the combinatorics of strong chain conditions and the investigation of *principles of structural reflection* formulated by Bagaria.