| Résume | Infinitary logics arose in the 60s as a natural generalization of first order logic. With the role of compactness played by consistency properties, L_omega_1_omega rapidly became a prominent example. I will argue that Boolean valued models are a natural semantics for arbitrary logics L_kappa_lambda. These results will allow us to present forcing as the set theoretic perspective of consistency properties, giving a more gentle introduction to the technique. Finally, some ideas and results relating inner models of set theory, infinitary logics and forcing will be presented. This is joint work with M. Viale. |
