About the course
The course covers:
• Fundamentals and set theory: The Zermelo-Fraenkel axioms of set theory, elementary theory for cardinals and ordinals.
Equivalent formulations of the axiom of choice and its applications in analysis and algebra.
• Structures and models: Isomorphisms and embeddings, complete theories, elementary equivalence and elementary embedding, Löwenheim-Skolem's theorems, categoricality, applications on algebraic theories and non-standard analysis.
• Computability and incompleteness: Models of computation, classes of computable functions, decidable and irreversible problems, Gödel coding and Gödel's incompleteness theorem.