Monday (13:30-15:00, room F420), Wednesday (10:00-11:30, room D436), Thursday (15:15-16:45, room M801).

Monday, June 2nd: Exercise session, 10:00-11:30, room H303.

Monday, June 23rd: Exercise session, 10:00-11:30, room D404.

Monday, June 30th: Exercise session, 10:00-11:30, room D431.

Abstract. Closely related to Algebra, Model theory is a branch of Mathematical logic that studies the links between a structure (eg a group, a field, or a graph) and its logical properties. The course aims at giving a self contained introduction to the subject. Typical topics that will be introduced:
- language and structure,
- formula and satisfaction,
- notion of proof and the Completeness Theorem,
- Compactness Theorem of first order logic, ultraproduct of structures,
- elementary extension, saturated extension,
- quantifier elimination,
- algebraically closed field,
- real closed ordered field and o-minimal structure.

Lecture notes. Preliminary version.

May 9th: Definition 1.16 (compatible terms) modified, Definition 2.12 (generalisation rule) modified, Exercise 2.15 added.
May 23th: Definition 2.9 (E-axiom) modified.

Exercise sheets. 1. Structures, 2. Formulas, 3. Proofs, 4. Products, 5. Compactness, 6. Ordinals, 7. Elementary extensions, 8. Companions, 9. Axiomatisation, 10. Quantifier elimination, 11. Categoricity, 12. Definability.

Correction. 2. Formulas, 3. Proofs, 4. Products, 5. Compactness, 6. Ordinals, 7. Elementary extensions.

References.
Alexander Prestel, Einführung in die mathematische Logik und Modelltheorie, 1992 (Bibliothek: lbs 800/p72a), English translation with more exercises:
Alexander Prestel and Charles Delzell, Mathematical logic and model theory: a brief introduction, Springer, 2011. (lbs 800/p72c).
Zoé Chatzidakis, Cours de logique, École Normale Supérieure, 2013.
François Loeser, Un premier cours de logique, 2010.

Examination.
Tuesday 29.07.2014 from 10:00 to 13:00, room D431.