This biannual learning unit is being organized in 2024-2025
Teacher(s)
Language
French
> English-friendly
> English-friendly
Content
This activity aims to explore the mathematical formalization of logic in terms of inference rules (sequents), lattices (and, in particular, Heyting and Boolean algebras), models (topological and Kripke) and quantifier systems (for predicative logic). The following contents are covered in the course:
- Propositional logic, Gentze sequents, Lindenbaum-Tarski algebra.
- Lattices, Heyting algebras and Boolean algebras.
- Models of propositional logic and the theorems of validity, consistency and completeness.
- Dedekind and Stone representation theorems,
- Ideals and filters of an ordered set, the extension-exclusion lemma and the axiom of choice.
- Quantifier systems and predicative logic.
- Propositional logic, Gentze sequents, Lindenbaum-Tarski algebra.
- Lattices, Heyting algebras and Boolean algebras.
- Models of propositional logic and the theorems of validity, consistency and completeness.
- Dedekind and Stone representation theorems,
- Ideals and filters of an ordered set, the extension-exclusion lemma and the axiom of choice.
- Quantifier systems and predicative logic.
Teaching methods
Supervised learning activities consist of lecture sessions. Group discussion and the resolution of exercises by students are integrated into the lecture. The course aims to introduce fundamental concepts, to motivate them by showing examples and establishing results, to show the links with other courses in the Bachelor's program in Mathematical Sciences. The resolution of exercises aims to learn the basic techniques of sequent calculus, lattice theory and adjunctions between ordered sets.
Evaluation methods
The assessment aims to test knowledge and understanding of fundamental concepts, examples and results, the ability to construct coherent reasoning, mastery of the demonstration techniques introduced during the course. The assessment consists of a final exam. Each student can choose between an oral exam and a written exam. In any case, the student proposes a first question that he or she develops and then the teacher asks other questions to test a fairly broad spectrum of skills. To establish the final grade, the final exam and active participation in the course will be taken into account (questions asked, solutions to exercises presented in class).
Other information
The course is biennial and will be activated in 2024-2025.
Online resources
Moodle site. The site contains the course syllabus, including many exercises that are integrated into each chapter.
Bibliography
F. W. Lawvere, R. Rosebrugh, Sets for Mathematics, Cambridge University Press, 2003
S. Mac Lane, I. Moerdijk, Sheaves in Geometry and Logic, Springer 1992
S. Mac Lane, I. Moerdijk, Sheaves in Geometry and Logic, Springer 1992
Teaching materials
- Syllabus LMAT1235
Faculty or entity
