Entry requirements

120 credit points with the courses Algebraic Structures, Logic II and Set Theory.

Learning outcomes

In order to pass the course the student should be able to

• describe various methods for constructing new models;
• carry out quantifier elimination;
• characterise theories with a unique and theories with finitely many infinite countable models;
• given a model theoretic property, decide whether a concrete structure has this property or not, and explain why;
• construct concrete examples to illustrate important model theoretic notions;
• outline proofs of important theorems of the course and explain the main ideas of the proofs;
• give examples of algebraic applications of model theory.

Content

The compactness theorem via the ultra product method. Elementary substructures and extensions, categoricity, elimination of quantifiers, types, Stone spaces, algebraic closure in structures. Saturated structures, atomic structures, prime models, omitting types, characterisations of theories with a unique infinite countable model, theories with finitely many infinite countable models, minimal theories, dimension, total categoricity, Steinitz' theorem and its model theoretic version. Introduction to model theoretic stability theory. Applications to algebra.

Instruction

Lectures and problem solving sessions.

Assessment

Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.