Characterizing Large Cardinals in Terms of Löwenheim-Skolem and Weak Compactness Properties

Explore a mathematical lecture on characterizing large cardinals using Löwenheim-Skolem and weak compactness properties. Delve into the intricate world of strong logics and their relationship to large cardinals, focusing on fragments of infinitary second-order logic. Discover how a cardinal kappa's strength can be determined by the Löwenheim-Skolem property for specific logic fragments. Examine recent research findings on weak compactness properties and their connection to Shelah cardinals. Learn about the conditions under which theories in the dual of certain logic fragments have models, and how this relates to cardinal characteristics. Gain insights into advanced topics in set theory and logic during this 44-minute talk presented at the Workshop on "Determinacy, Inner Models and Forcing Axioms" at the Erwin Schrödinger International Institute for Mathematics and Physics.