General information 
Course unit name: Advanced Model Theory
Course unit code: 569075
Academic year: 20212022
Coordinator: Enrique Casanovas Ruiz Fornells
Department: Department of Mathematics and Computer Science
Credits: 5
Single program: S
Estimated learning time 
Total number of hours 125 
Facetoface and/or online activities 
42 
 Lecture with practical component 
Facetoface 
42 
Supervised project 
18 
Independent learning 
65 
Recommendations 
Further recommendations

Competences to be gained during study 
To be able to carry out independent study of standard textbooks and journal articles on model theory.

Learning objectives 
Referring to knowledge
Referring to abilities, skills

Teaching blocks 
1. PRELIMINARIES
* Back and forth, saturation, the monster model, quantifier elimination, modelcompleteness, and omegacategoricity.
2. DEFINABILITY
*
Definable, typedefinable and invariant relations. Beth and Svenonious theorems. Definable and algebraic closure. Imaginaries.
3. PREGEOMETRIES
*
Closure operators with exchange. Independence, basis and dimension. Modularity. Vector spaces.
4. RANKS
*
CantorBendixson rank. Morley rank. Omegastability and superstability. Strongly minimal sets. Algebraically closed fields.
5. PRIME MODELS
* Omitting types. Prime and atomic models. Indiscernibles. Two cardinal theorems.
6. CATEGORICITY
*
Morley and BaldwinLachlan’s theorems.
Teaching methods and general organization 

Official assessment of learning outcomes 
Weekly exercises. 40 %
Examinationbased assessment Final examination 
Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
E. Casanovas Advanced Model Theory.
These Lecture Notes will be delivered during the course. 
E. Casanovas. Teoría de Modelos (Lecture Notes). 1999.
Available at http://www.ub.es/modeltheory/casanovas 
C.C. Chang and H.J. Keisler. Model Theory. North Holland PC, 3rd ed. 1990.
W. Hodges. Model Theory. Cambridge UP 1993.
D. Lascar. Stability in Model Theory. Longman Sci. and Tech. 1987.
D. Lascar. La théorie des modèles en peu de maux. Cassini, Paris 2009.
D. Marker. Model Theory: an introduction. Springer 2002.
D. Marker, M. Messmer and A. Pillay. Introduction to the Model Theory of Fields. Lecture Notes in Logic 5. Springer 1996.
A. Pillay. An introduction to Stability Theory. Oxford UP 1983.
A. Pillay. Geometrical Stability Theory. Oxford UP. 1996.
B. Poizat. Cours de théorie des modèles. Offilib. Villeurbanne 1985.
K. Tent and M. Ziegler. A course in Model Theory. Lecture Notes in Logic 40. Cambridge UP 2012.