Subject code: BMA-LOTD-301.05, BMI-LOTD-301E.01	
Subject name: Advanced Model Theory	
Lecturer: Zalán Gyenis	

Goal of instruction:

The goal of the class is to discuss various topics from classical model theory of first order logic. Some preliminary knowledge of (axiomatic) set theory and general mathematics is assumed.	

Subject content:

This course deals with model theory of classical first order logic and offers the following topics.  

1. Basics, fundamental theorems: Compactness, Completeness, Löwenheim--Skolem
2. Differences between finite and infinite, Elementary equivalence 
3. Ehrenfeucht-Fraissé game, Quantifier elimination
4. Ultraproduct construction
5. Axiomatizability
6. Types, Saturation, Universality
7. Beth definability, Omitting types
8. Bits of classification theory

The topics and the order of the topics can change depending on time and interest.	

Examination and evaluation system:

weekly homeworks (60%) + final oral exam (40%)	

Literature:

Chang, C.C., Keisler, H.J.: Model Theory; North-Holland, Amsterdam, 1990
Hodges, W.: Model theory; Cambridge University Press, 1997
Marker, D.: Model theory, An introduction; GMT, 217, Springer-Verlag, NY, 2002