Logic II, 7.5 credits

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.

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