Logic II : Computability, Set Theory, and Model Theory (Fall 2025)
Masters level course, Stockholm University, Sweden, 2025
Logic II is a second level logic course, giving an introduction to major topics of modern mathematical logic. It consists of three main parts:
- Computability and incompleteness: models of computability; (un)decidability and (un)computability; coding of logic, and Gödel’s incompleteness theorems.
- Axiomatic foundations: Zermelo–Fraenkel set theory, and the development of mathematics therein, including ordinals, cardinals, transfinite recursion, the axiom of choice and its applications, and first independence results
- Model theory: structures and isomorphisms, elementary equivalence and embeddings, the Löwenheim–Skolem theorems, categoricity, back-and-forth arguments, and applications/examples including non-standard analysis
Resources
The course textbook is the following book:
R. Cori, D. Lascar, 2001, Mathematical Logic, A Course with Exercises, Part II: Recursion Theory, Gödel’s Theorems, Set Theory, Model Theory, Oxford University Press.
I also highly Jeremy Avigad’s excellent book:
Avigad, Jeremy. 2022. Mathematical Logic and Computation. Cambridge: Cambridge University Press.