Mathematical Logic

Program

The official syllabus is available.

• Propositional logic: language, deduction system, semantics, soundness, completeness;
• First-order logic: syntax, semantics, soundness, completeness, compactness;
• Set theory: fundamental axioms, ordinals, cardinals, transfinite induction, axiom of choice, continuum hypothesis;
• Computability: computable functions, λ-calculi, simple theory of types;
• Constructive mathematics: intuitionistic logic, propositions as types, normalisation;
• Limiting results: Peano arithmetic, Gödel’s incompleteness theorems, natural incompleteness results.

The slides of the course are available: select the right academic year

• 2025/26 (printer-friendly version); 2025/26 (screen-friendly version)
• 2024/25 (printer-friendly version); 2024/25 (screen-friendly version)
• 2023/24 (printer-friendly version)
• 2022/23 (printer-friendly version)
• 2021/22
• 2020/21
• 2019/20
• 2018/19
• 2017/18
• 2016/17
• 2015/16

Here are some exercises on natural deduction.
The official online course for the academic year 2021/22 is available: please carefully read the introductory notes!

The non-official videos are available in the video page.
Note that this course on YouTube differs from the online course!

Assignments

Results 2024/25