Student Model Theory Seminar (Invited Address)

Title: An introduction to infinitary first-order (and propositional) logic

Abstract: What happens to first-order logic if you allow the logical connectives and/or quantifiers to be infinitely long? It turns out that many of the standard tools and results (e.g., compactness) either break or trivialize, while new interesting phenomena arise. Indeed, infinitary propositional logic is already quite interesting, and is closely related to (in some sense, equivalent to) topology. Moreover, the interaction between propositional and first-order plays a central role in infinitary logic, and leads to the application of tools from topology and group actions to model theory. This talk will survey a proper subset of these topics, such as the Scott isomorphism theorem, omitting types theorem, and Lopez-Escobar theorem.