Maximilian Vranjes: The Proofs of the Compactness Theorem of First Order Logic

Abstract:

The goal of this thesis will be to explore three areas of mathematics through the lens of a single theorem — the compactness theorem. These areas include filters and ultraproducts, Boolean algebras and topologies, and Henkin constructions. The thesis will also be clear on the role of the axiom of choice in each of these methods.